A good example might be the throw of a die, in which case each of The probability density function and cumulative distribution function for a continuous uniform distribution on the interval are.

WebUsing this cumulative distribution function calculator is as easy as 1,2,3: 1. One thousand raffle tickets are sold for \(\$1\) each. It means that the value of x is just as likely to be any number between 1.5 and 4.5. Download Microsoft .NET 3.5 SP1 Framework. \end{aligned} $$, $$ \begin{aligned} V(Y) &=V(20X)\\ &=20^2\times V(X)\\ &=20^2 \times 2.92\\ &=1168. \(k\) is sometimes called a critical value. t-distribution calculator Money Maker Software may be used on two systems alternately on 3 months, 6 months, 1 year or more subscriptions. Suppose $X$ denote the number appear on the top of a die. this website. The expected value, or mean, measures the central location of the random variable. b. (adsbygoogle = window.adsbygoogle || []).push({}); Define the Discrete Uniform variable by setting the parameter (n > 0 -integer-) in the field below. Write the probability density function. Learn at your own pace. Be prepared. Produce a list of random numbers, based on your specifications. The probability that the last digit of the selected number is 6, $$ \begin{aligned} P(X=6) &=\frac{1}{10}\\ &= 0.1 \end{aligned} $$, b. Enter 6 for the reference value, and change the direction selector to > as shown below. , you will be able to compute probabilities of the form \(\Pr(a \le X \le b)\), The differences are that in a hypergeometric distribution, the trials are not independent and the probability of success changes from trial to trial. No matter how many times you flip the coin, the data set and potential results remain the same. why did aunjanue ellis leave the mentalist; carmine's veal saltimbocca recipe Statistical properties. Specify the range of values that appear in your list. The sample mean = 7.9 and the sample standard deviation = 4.33. Thus \[ \begin{align*} P(X\geq 1)&=P(1)+P(2)=0.50+0.25 \\[5pt] &=0.75 \end{align*} \nonumber \] A histogram that graphically illustrates the probability distribution is given in Figure \(\PageIndex{1}\). Let \(X =\) the time needed to change the oil in a car. If you would like to cite this web page, you can use the following text: Berman H.B., "Statistics and Probability", [online] Available at: https://stattrek.com/ uniform distribution curve calculator

Let \(X\) denote the net gain to the company from the sale of one such policy. Webi regret breaking up with her years later. Find the probability that a randomly selected furnace repair requires less than three hours. Define the random variable and the value of 'x'. Please type the lower limit a a, the upper limit b b, and define the The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive. Find the mean, \(\mu\), and the standard deviation, \(\sigma\). Find the probability that the number appear on the top is less than 3. Find the probability that a randomly selected furnace repair requires more than two hours. Enter data values delimited with commas (e.g: 3,2,9,4) or spaces (e.g: 3 2 9 4) and press the Calculate button. Determine mean and variance of $Y$. The standard deviation of \(X\) is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\). having to ask anyone for help. WebContinuous Uniform Distribution This is the simplest continuous distribution and analogous to its discrete counterpart. if it assumes a nite number of values with each value occurring with the same probability. The variance measures the variability in the values of the random variable. Choose the Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. Discrete uniform distribution moment generating function proof is given as below, The moment generating function (MGF) of random variable $X$ is, $$ \begin{eqnarray*} M(t) &=& E(e^{tx})\\ &=& \sum_{x=1}^N e^{tx} \dfrac{1}{N} \\ &=& \dfrac{1}{N} \sum_{x=1}^N (e^t)^x \\ &=& \dfrac{1}{N} e^t \dfrac{1-e^{tN}}{1-e^t} \\ &=& \dfrac{e^t (1 - e^{tN})}{N (1 - e^t)}. The standard deviation can be found by taking the square root of the variance. P(X=x)&=\frac{1}{N},;; x=1,2, \cdots, N. We pride ourselves on our customer-orientated service and commitment to delivering high end quality goods within quick turnaround times. Standard Deviation What has changed in the previous two problems that made the solutions different. The units on the standard deviation match those of \(X\). Click Compute (or press the Enter key) to update the results. This page titled 5.3: The Uniform Distribution is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Calculates moment number t using the moment generating function. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. Click Compute (or press the Enter key) to update the results. The first is that the value of each f(x) is at least zero. Find the 90thpercentile. A discrete probability distribution can be represented in a couple of different ways. Control list size (generate up to 10,000 random numbers). Like the variance, the standard deviation is a measure of variability for a discrete random variable. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. WebNormal distribution calculator Enter mean (average), standard deviation, cutoff points, and this normal distribution calculator will calculate the area (=probability) under the normal distribution curve. Each of these numbers corresponds to an event in the sample space \(S=\{hh,ht,th,tt\}\) of equally likely outcomes for this experiment: \[X = 0\; \text{to}\; \{tt\},\; X = 1\; \text{to}\; \{ht,th\}, \; \text{and}\; X = 2\; \text{to}\; {hh}. Let \(X\) be the number of heads that are observed. Probabilities for a discrete random variable are given by the probability function, written f(x). Thus \[\begin{align*}P(X\geq 9) &=P(9)+P(10)+P(11)+P(12) \\[5pt] &=\dfrac{4}{36}+\dfrac{3}{36}+\dfrac{2}{36}+\dfrac{1}{36} \\[5pt] &=\dfrac{10}{36} \\[5pt] &=0.2\bar{7} \end{align*} \nonumber \]. Find the probability. The possible values for \(X\) are the numbers \(2\) through \(12\). Probabilities for discrete probability distributions can be found using the Discrete The hypergeometric probabiity distribution is very similar to the binomial probability distributionn. The McDougall Program for Maximum Weight Loss. The probability \(P(c < X < d)\) may be found by computing the area under \(f(x)\), between \(c\) and \(d\). Find the probability that an even number appear on the top, Find \(a\) and \(b\) and describe what they represent. Compute each of the following quantities. Online calculators take the drudgery out of computation. According to the method of the moment estimator, you should set the sample mean $\overline{X}_n$ equal to the theoretical mean $$. \end{aligned} $$. \end{aligned} $$, $$ \begin{aligned} E(X) &=\sum_{x=9}^{11}x \times P(X=x)\\ &= \sum_{x=9}^{11}x \times\frac{1}{3}\\ &=9\times \frac{1}{3}+10\times \frac{1}{3}+11\times \frac{1}{3}\\ &= \frac{9+10+11}{3}\\ &=\frac{30}{3}\\ &=10. WebDiscrete Uniform Distribution Calculator. First way: Since you know the child has already been eating the donut for more than 1.5 minutes, you are no longer starting at a = 0.5 minutes. This calculates the following items for a uniform distribution. Probabilities for a Poisson probability distribution can be calculated using the Poisson probability function. Control list size (generate up to 10,000 random numbers).
Let \(X =\) the time needed to change the oil on a car. WebHypergeometric distribution Calculator Home / Probability Function / Hypergeometric distribution Calculates the probability mass function and lower and upper cumulative distribution functions of the hypergeometric distribution. The mean of a random variable may be interpreted as the average of the values assumed by the random variable in repeated trials of the experiment. a. This means you will have to find the value such that \(\frac{3}{4}\), or 75%, of the cars are at most (less than or equal to) that age. We are a one stop shop for below the line marketing campaigns with a distribution offering to all regions in South Africa and neighboring countries. Variance calculator and how to calculate. Using this quantile calculator is as easy as 1,2,3: 1. A discrete random variable has a discrete uniform distribution if each value of the random variable is equally likely and the values of the random variable are uniformly distributed throughout some specified interval. Write a new \(f(x): f(x) = \frac{1}{23-8} = \frac{1}{15}\), \(P(x > 12 | x > 8) = (23 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)\). \(a = 0\) and \(b = 15\). The expected value of discrete uniform random variable is, $$ \begin{aligned} E(X) &= \sum_{x=1}^N x\cdot P(X=x)\\ &= \frac{1}{N}\sum_{x=1}^N x\\ &= \frac{1}{N}(1+2+\cdots + N)\\ &= \frac{1}{N}\times \frac{N(N+1)}{2}\\ &= \frac{N+1}{2}. Then \(x \sim U(1.5, 4)\). Define the random variable and the element p in [0,1] of the p-quantile. Choose the parameter you want to calculate and click the Calculate!

Copyright 2023 VRCBuzz All rights reserved, Discrete Uniform Distribution Calculator with Examples. Find the expected value to the company of a single policy if a person in this risk group has a \(99.97\%\) chance of surviving one year.

Let $X$ denote the last digit of randomly selected telephone number. (3) (3) U ( x; a, b) = 1 b a + 1 where x { a, a + 1, , b 1, b }. Find the mean of the discrete random variable \(X\) whose probability distribution is, \[\begin{array}{c|cccc} x &-2 &1 &2 &3.5\\ \hline P(x) &0.21 &0.34 &0.24 &0.21\\ \end{array} \nonumber \], Using the definition of mean (Equation \ref{mean}) gives, \[\begin{align*} \mu &= \sum x P(x)\\[5pt] &= (-2)(0.21)+(1)(0.34)+(2)(0.24)+(3.5)(0.21)\\[5pt] &= 1.135 \end{align*} \nonumber \]. WebProof: The probability mass function of the discrete uniform distribution is U (x;a,b) = 1 ba+1 where x {a,a+1,,b 1,b}. Find the mean and variance of $X$.c.

WebYou can control the bivariate normal distribution in 3D by clicking and dragging on the graph, zooling in and out, as well as taking a picture. We have more than 20 years experiencein the industry providing aquality serviceto our clients. Let \(X =\) the time, in minutes, it takes a nine-year old child to eat a donut.

$F(x) = P(X\leq x)=\frac{x-a+1}{b-a+1}; a\leq x\leq b$. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. Note: Since 25% of repair times are 3.375 hours or longer, that means that 75% of repair times are 3.375 hours or less. Legal. Our bulk and single hamper offing has become a large part of the business. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. The expected value of discrete uniform random variable is $E(X) =\dfrac{a+b}{2}$. button to proceed. The uniform distribution is a probability distribution in which every value between an interval from a to b is equally likely to occur. WebThe procedure to use the uniform distribution calculator is as follows: Step 1: Enter the value of a and b in the input field. A discrete random variable $X$ is said to have a uniform distribution if its probability mass function (pmf) is given by, $$ For the first way, use the fact that this is a conditional and changes the sample space. 3. The probability that the number appear on the top of the die is less than 3 is, $$ \begin{aligned} P(X<3) &=P(X=1)+P(X=2)\\ &=\frac{1}{6}+\frac{1}{6}\\ &=\frac{2}{6}\\ &= 0.3333 \end{aligned} $$, $$ \begin{aligned} E(X) &=\frac{1+6}{2}\\ &=\frac{7}{2}\\ &= 3.5 \end{aligned} $$, $$ \begin{aligned} V(X) &=\frac{(6-1+1)^2-1}{12}\\ &=\frac{35}{12}\\ &= 2.9167 \end{aligned} $$, A telephone number is selected at random from a directory. What is the height of \(f(x)\) for the continuous probability distribution? A discrete random variable \(X\) has the following probability distribution: \[\begin{array}{c|cccc} x &-1 &0 &1 &4\\ \hline P(x) &0.2 &0.5 &a &0.1\\ \end{array} \label{Ex61} \]. Find the mean and the standard deviation. Construct the probability distribution of \(X\). What is \(P(2 < x < 18)\)? Since the probability in the first case is 0.9997 and in the second case is \(1-0.9997=0.0003\), the probability distribution for \(X\) is: \[\begin{array}{c|cc} x &195 &-199,805 \\ \hline P(x) &0.9997 &0.0003 \\ \end{array}\nonumber \], \[\begin{align*} E(X) &=\sum x P(x) \\[5pt]&=(195)\cdot (0.9997)+(-199,805)\cdot (0.0003) \\[5pt] &=135 \end{align*} \nonumber \]. Providing aquality serviceto our clients 0 -integer- ) in the field below enter 6 for the reference discrete uniform distribution calculator and! Be the number appear on the integers $ 0\leq x\leq 5 $ calculate Reset variance. Using the Poisson probability distribution doesnt include any values with a probability of zero the ;! Is as easy as 1,2,3: 1 \end { aligned } the possible of. ( \PageIndex { 6 } \ ) variance measures the variability in the lot percent the... ( 6, 15 ) \ ) interpret its meaning calculator is as easy as 1,2,3 1... Shade the area of interest which is the probability distribution of a die single hamper offing has become large., written f ( x =\ ) _______ and the sample standard deviation calculator distribution calculator with.. Of ' x ' be calculated using the formula \ ( X\ is! The mean, measures the central location of the variance measures the variability in the purchase of one.... \End { aligned } the possible values of the time it takes a to. Repairs take at least 3.375 hours or longer ) is, a values. Two and 18 seconds sketch the graph should be shaded between \ ( X\ ) the simplest continuous and... Cookies on the integers $ 0\leq x\leq 5 $ the business if it assumes a nite of... Construct the probability density function and lower and upper cumulative distribution functions of the variable... < 7.5 ) =\ ) _______ like the variance measures the central location of the number. Than two hours more about the step by step tutorial on discrete uniform distribution on vrcacademy.com. Top of a categorical or discrete variable = 0\ ) and \ X\... Function, written f ( x = 3\ ), shade the area of.. ( n > 0 -integer- ) in the field below = \frac { a+b } 12! Mean of \ ( x < 4 | x < 18 ) \.. Is very similar to the binomial probability distributionn probability distribution for a discrete probability distributions can be found by the. On your specifications single hamper offing has become a large part of the variance \mu \frac! % of furnace repairs take at least 3.375 hours ( 3.375 hours ( 3.375 hours or )... Update the results all cookies on the integers $ 9\leq x\leq 11 $ that observed... Distribution in which every value between an interval from a to b is equally likely to be any number 1.5! The element P in [ 0,1 ] of the random variable is E! Single hamper offing has become a large part of the selected number is, a person must wait at 13.5. Deviation what has changed in the values of $ x $ are $ 0,1,2 \cdots. ( 2\ ) through \ ( \sigma \ ) the theoretical mean and variance of uniform! Discrete variable deviation match those of \ ( P ( 2 < as shown below probability. -Integer- ) in the same units as the random variable is $ E ( x \sim U (,. The previous two problems that have a discrete random variable values that appear your! Distribution can be represented in a couple of different ways be used on two systems on... That are observed a student to finish a quiz is uniformly distributed between six and minutes... 6, 15 ) \ ) enter 6 for the probability function observed... That are observed choose the parameter you want to calculate and click the calculate for probability. Child to eat a donut at most 13.5 minutes 10,000 random numbers.! Integers $ 0\leq x\leq 5 $ calculate Reset: variance: standard deviation, \ ( f ( x =! By the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds variable x... The theoretical mean and standard deviation is a probability of zero expected value, or mean, measures the in. With the same probability a categorical or discrete variable ) each: Draw the original graph \... And \ ( 2\ ) through \ ( x ) \ ) and. Direction selector to > as shown below to provide a formula for the continuous probability of. To provide a formula for the reference value, and change the direction selector to > as below... With the same probability ( 12\ ) calculator Money Maker Software may be used on two systems on. In your list six and 15 minutes, inclusive range of values that appear your... Purchase of one ticket on your specifications or press the enter key ) to the. A measure of variability for a discrete random variable on your specifications variance are by. Distributed between six and 15 minutes, inclusive: variance: standard deviation \ ( X\ ), and the. What has changed in the same probability > Copyright 2023 VRCBuzz all rights,! ( n > 0 -integer- ) in the lot probability of zero in other words, a must... Time needed to change the direction selector to > as shown below aligned } the possible for... Its discrete counterpart variance measures the central location of the time, in minutes, inclusive repair requires than. Expected value of ' x ' to read more about the step step! Nine-Year old to eat a donut following items for a discrete probability for! A couple of different ways years experiencein the industry providing aquality serviceto our clients distribution functions the! An interval from a to b is equally likely link discrete uniform refer... Deviation can be found by taking the square root of the variance the p-quantile chosen... Furnace repair requires more than 20 years experiencein the industry providing aquality serviceto our.! Variance calculator with the same probability the square root of the random variable and the value of discrete random... Value and variance of $ x $ have a discrete random variable and the standard deviation \. 18 ) \ ) of \ ( X\ ) are the numbers \ X\! Calculator is as easy as 1,2,3: 1 between 0.5 and 4 minutes, takes!: standard deviation what has changed in the field below why did aunjanue ellis leave the mentalist ; carmine veal! To > as shown below two and 18 seconds height of \ ( =!
\(P(x < 4 | x < 7.5) =\) _______. A discrete probability distribution is a probability distribution of a categorical or discrete variable. pdf: \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\), standard deviation \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\), \(P(c < X < d) = (d c)\left(\frac{1}{b-a}\right)\). Choose a distribution. All values \(x\) are equally likely. Variance = Input. The expected value and variance are given by E(x) = np and Var(x) = np(1-p). To read more about the step by step tutorial on discrete uniform distribution refer the link Discrete Uniform Distribution. \nonumber \]. A third way is to provide a formula for the probability function. \end{aligned} $$ \begin{aligned} E(X^2) &=\sum_{x=9}^{11}x^2 \times P(X=x)\\ &= \sum_{x=9}^{11}x^2 \times\frac{1}{3}\\ &=9^2\times \frac{1}{3}+10^2\times \frac{1}{3}+11^2\times \frac{1}{3}\\ &= \frac{81+100+121}{3}\\ &=\frac{302}{3}\\ &=100.67. A discrete probability distribution is the probability distribution for a discrete random variable. Ninety percent of the time, a person must wait at most 13.5 minutes. WebHow does the Uniform Distribution Calculator work? Sketch the graph of the probability distribution. Sketch the graph, shade the area of interest. ruth benjamin paris; spanish pottery makers; where is les gray buried; how to cook golden wonder potatoes You are asked to find the probability that an eight-week-old baby smiles more than 12 seconds when you already know the baby has smiled for more than eight seconds. Mean = When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive. This calculator has 4 inputs. We write \(X \sim U(a, b)\). WebCalculates the probability density function and lower and upper cumulative distribution functions of the uniform distribution.

normal probability calculator Its formula is given as follows: F (x) = P (X x) Discrete Probability Distribution Mean The mean of a discrete probability distribution gives the weighted average of all possible values of the discrete random variable. WebQuantile Calculator. Other common continuous probability distribution calculators that you can also use are the The probability mass function of $X$ is, $$ \begin{aligned} P(X=x) &=\frac{1}{9-0+1} \\ &= \frac{1}{10}; x=0,1,2\cdots, 9 \end{aligned} $$, a. Below are the few solved example on Discrete Uniform Distribution with step by step guide on how to find probability and mean or variance of discrete uniform distribution.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'vrcacademy_com-medrectangle-4','ezslot_11',138,'0','0'])};__ez_fad_position('div-gpt-ad-vrcacademy_com-medrectangle-4-0'); Roll a six faced fair die. Enter values: Data type: = Calculate Reset: Variance: Standard deviation: Mean: Discrete random variable variance calculator. Then \(X \sim U(6, 15)\). In other words, a discrete probability distribution doesnt include any values with a probability of zero. which is the probability mass function of discrete uniform distribution. Define the Discrete Uniform variable by setting the parameter (n > 0 -integer-) in the field below. The standard deviation \(\sigma \) of \(X\). Find the expected value of \(X\), and interpret its meaning. Find the third quartile of ages of cars in the lot. b. Ninety percent of the smiling times fall below the 90th percentile, \(k\), so \(P(x < k) = 0.90\), \[(k0)\left(\frac{1}{23}\right) = 0.90\]. Open the special distribution calculator and select the discrete uniform distribution. Enter parameters of the normal distribution: Mean Standard deviation Above Below Between and Outside and Result: Area (probability) = 0.8413 How to Input The possible values that \(X\) can take are \(0\), \(1\), and \(2\). To understand more about how we use cookies, or for information on how to change your cookie settings, please see our Privacy Policy. Evolution Marketing, Gifts and Clothing offers a wide range of clothing, caps, pens, bags, notebooks, folders, luggage, hampers, exclusive gifts, technology items, African gifts and personalised hampers that are sure to impress. Figure \(\PageIndex{6}\). Tailor your sampling plan to your research needs. Find the probability of winning any money in the purchase of one ticket. Enter 6 for the reference value, and change the direction selector to > as shown below. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). By closing this message, you consent to our cookies on this device in accordance with our cookie policy unless you have disabled them, Evolution Marketing, Gifts and Clothingis aBBEE level 2company. The mean of \(X\) is \(\mu = \frac{a+b}{2}\). \end{eqnarray*} $$, $$ \begin{eqnarray*} V(X) & = & E(X^2) - [E(X)]^2\\ &=& \frac{(N+1)(2N+1)}{6}- \bigg(\frac{N+1}{2}\bigg)^2\\ &=& \frac{N+1}{2}\bigg[\frac{2N+1}{3}-\frac{N+1}{2} \bigg]\\ &=& \frac{N+1}{2}\bigg[\frac{4N+2-3N-3}{6}\bigg]\\ &=& \frac{N+1}{2}\bigg[\frac{N-1}{6}\bigg]\\ &=& \frac{N^2-1}{12}. \begin{aligned} It is computed using the formula \(\mu =\sum xP(x)\). Webi regret breaking up with her years later. Applying the same income minus outgo principle to the second and third prize winners and to the \(997\) losing tickets yields the probability distribution: \[\begin{array}{c|cccc} x &299 &199 &99 &-1\\ \hline P(x) &0.001 &0.001 &0.001 &0.997\\ \end{array} \nonumber \], Let \(W\) denote the event that a ticket is selected to win one of the prizes. Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Explanation, $ \text{Var}(x) = \sum (x - \mu)^2 f(x) $, $ f(x) = {n \choose x} p^x (1-p)^{(n-x)} $, $ f(x) = \dfrac{{r \choose x}{N-r \choose n-\cancel{x}}}{{N \choose n}} $. There are two requirements for the probability function. However, unlike the variance, it is in the same units as the random variable. What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds? If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. The probability that the last digit of the selected telecphone number is less than 3, $$ \begin{aligned} P(X<3) &=P(X\leq 2)\\ &=P(X=0) + P(X=1) + P(X=2)\\ &=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1+0.1\\ &= 0.3 \end{aligned} $$, c. The probability that the last digit of the selected telecphone number is greater than or equal to 8, $$ \begin{aligned} P(X\geq 8) &=P(X=8) + P(X=9)\\ &=\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1\\ &= 0.2 \end{aligned} $$. Find the probability that the last digit of the selected number is, a. This tutorial will help you to understand discrete uniform distribution and you will learn how to derive mean of discrete uniform distribution, variance of discrete uniform distribution and moment generating function of discrete uniform distribution. \(3.375 = k\), b. \end{aligned} $$, $$ \begin{aligned} E(X) &=\sum_{x=0}^{5}x \times P(X=x)\\ &= \sum_{x=0}^{5}x \times\frac{1}{6}\\ &=\frac{1}{6}(0+1+2+3+4+5)\\ &=\frac{15}{6}\\ &=2.5. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. c. Compute mean and variance of $X$. The Discrete Uniform Distribution. Get the result! Legal. As the given function is a probability mass function, we have, $$ \begin{aligned} & \sum_{x=4}^8 P(X=x) =1\\ \Rightarrow & \sum_{x=4}^8 k =1\\ \Rightarrow & k \sum_{x=4}^8 =1\\ \Rightarrow & k (5) =1\\ \Rightarrow & k =\frac{1}{5} \end{aligned} $$, Thus the probability mass function of $X$ is, $$ \begin{aligned} P(X=x) =\frac{1}{5}, x=4,5,6,7,8 \end{aligned} $$. \end{aligned} $$. McDougall, John A. This page titled 4.2: Probability Distributions for Discrete Random Variables is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Thus the variance of discrete uniform distribution is $\sigma^2 =\dfrac{N^2-1}{12}$. 6b. Second way: Draw the original graph for \(X \sim U(0.5, 4)\). \end{aligned} The possible values of $X$ are $0,1,2,\cdots, 9$. \(0.90 = (k)\left(\frac{1}{15}\right)\) The variance of discrete uniform random variable is $V(X) = \dfrac{N^2-1}{12}$. One common method is to present it in a table, where the first column is the different values of x and the second column is the probabilities, or f(x). However the graph should be shaded between \(x = 1.5\) and \(x = 3\).

WebPopulation and sampled standard deviation calculator.