Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. Copyright (c) 2006-2016 SolveMyMath. b. Find the probability that an even number appear on the top, c. Compute mean and variance of $X$. c. Find the probability that $X\leq 6$. Suppose $X$ denote the number appear on the top of a die. Uniform (Discrete) Distribution. The Discrete uniform distribution, as the name says is a simple discrete probability distribution that assigns equal or uniform probabilities to all values that the random variable can take. Using the Binomial Probability Calculator $P(X=x)=k$ for $x=4,5,6,7,8$, where $k$ is constant. © VrcAcademy - 2020About Us | Our Team | Privacy Policy | Terms of Use. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. Discrete Random Variable Calculator Online probability calculator to find expected value E (x), variance (σ 2) and standard deviation (σ) of discrete random variable from number of outcomes. \end{aligned} $$, Mean of discrete uniform distribution $X$ is, $$ \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. Then the mean of discrete uniform distribution $Y$ is, $$ \begin{aligned} E(Y) &=E(20X)\\ &=20\times E(X)\\ &=20 \times 2.5\\ &=50. c. The mean of discrete uniform distribution $X$ is, $$ \begin{aligned} E(X) &=\frac{1+6}{2}\\ &=\frac{7}{2}\\ &= 3.5 \end{aligned} $$ Discrete Probability Distributions which contains calculators for the most important discrete distributions in mathematics. Below are the few solved examples on Discrete Uniform Distribution with step by step guide on how to find probability and mean or variance of discrete uniform distribution. Then the random variable $X$ take the values $X=1,2,3,4,5,6$ and $X$ follows $U(1,6)$ distribution. \end{aligned} $$, $$ \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=9.17-[2.5]^2\\ &=9.17-6.25\\ &=2.92. The probability that an even number appear on the top of the die is, $$ \begin{aligned} P(X=\text{ even number }) &=P(X=2)+P(X=4)+P(X=6)\\ &=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\\ &=\frac{3}{6}\\ &= 0.5 \end{aligned} $$ Let $X$ denote the number appear on the top of a die. 1. The probability that the last digit of the selected telecphone number is less than 3, $$ \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} $$. The probability mass function of $X$ is, $$ \begin{aligned} P(X=x) &=\frac{1}{9-0+1} \\ &= \frac{1}{10}; x=0,1,2\cdots, 9 \end{aligned} $$, a. Code to add this calci to your website Discrete Random Variable's expected value,variance and standard deviation are calculated easily. A random variable $X$ has a probability mass function You can refer below recommended articles for discrete uniform distribution theory with step by step guide on mean of discrete uniform distribution,discrete uniform distribution variance proof. The mean μ of a discrete random variable X is a number that indicates the … Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. Binomial Distribution Calculator Use this binomial probability calculator to easily calculate binomial cumulative distribution function and probability mass given the probability on a single trial, the number of trials and events. 4. Poisson Distribution The mean of discrete uniform distribution $X$ is, $$ \begin{aligned} E(X) &=\frac{4+8}{2}\\ &=\frac{12}{2}\\ &= 6. $$ \begin{aligned} E(X^2) &=\sum_{x=9}^{11}x^2 \times P(X=x)\\ &= \sum_{x=9}^{11}x^2 \times\frac{1}{3}\\ &=9^2\times \frac{1}{3}+10^2\times \frac{1}{3}+11^2\times \frac{1}{3}\\ &= \frac{81+100+121}{3}\\ &=\frac{302}{3}\\ &=100.67. This website uses cookies to ensure you get the best experience on our site and to provide a comment feature. Let the random variable $Y=20X$. The probability that the number appear on the top of the die is less than 3 is, $$ \begin{aligned} P(X < 3) &=P(X=1)+P(X=2)\\ &=\frac{1}{6}+\frac{1}{6}\\ &=\frac{2}{6}\\ &= 0.3333 \end{aligned} $$ b. All rights are reserved. \end{aligned} $$, Now, Variance of discrete uniform distribution $X$ is, $$ \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=100.67-[10]^2\\ &=100.67-100\\ &=0.67. So p ()1 =PM()=1= 1 3, p()2 = 1 2, p()3 = 1 6. \end{aligned} $$. 3. This list has either a finite number of members, or at most is countable. To analyze our traffic, we use basic Google Analytics implementation with anonymized data. \end{aligned} $$, Let $Y=20X$. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. The probability distribution of a discrete random variable X is a listing of each possible value x taken by X along with the probability P(x) that X takes that value in one trial of the experiment. b. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. All the integers $9, 10, 11$ are equally likely. \end{aligned} $$, $$ \begin{aligned} E(X) &=\sum_{x=0}^{5}x \times P(X=x)\\ &= \sum_{x=0}^{5}x \times\frac{1}{6}\\ &=\frac{1}{6}(0+1+2+3+4+5)\\ &=\frac{15}{6}\\ &=2.5. Some Examples include 'chance of three random points on a plane forming an acute triangle', 'calculating mean area of polygonal region formed by random oriented lines over a plane'. 6. Let $X$ denote the last digit of randomly selected telephone number. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. All the numbers $0,1,2,\cdots, 9$ are equally likely. A discrete random variable $X$ is said to have uniform distribution with parameter $a$ and $b$ if its probability mass function (pmf) is given byeval(ez_write_tag([[580,400],'vrcacademy_com-medrectangle-3','ezslot_4',126,'0','0'])); $$f(x; a,b) = \frac{1}{b-a+1}; x=a,a+1,a+2, \cdots, b $$, $$P(X\leq x) = F(x) = \frac{x-a+1}{b-a+1}; a\leq x\leq b $$, The expected value of discrete uniform random variable $X$ is, The variance of discrete uniform random variable $X$ is, A general discrete uniform distribution has a probability mass function, Distribution function of general discrete uniform random variable $X$ is, The expected value of above discrete uniform random variable $X$ is, The variance of above discrete uniform random variable $X$ is. This list has either a finite number of members, or at most is countable. Roll a six faced fair die. Thus the random variable $X$ follows a discrete uniform distribution $U(0,9)$. 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. (adsbygoogle = window.adsbygoogle || []).push({}); Discrete probability distributions arise in the mathematical description of probabilistic and statistical problems in which the values that might be observed are restricted to being within a pre-defined list of possible values.