# discrete probability distribution calculator

Use beelow discrete uniform distribution calculator to find probability and cumulative probabilities. 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. b. 1. 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'. \end{aligned} $$, And variance of discrete uniform distribution Y is,$$ \begin{aligned} V(Y) &=V(20X)\\ &=20^2\times V(X)\\ &=20^2 \times 2.92\\ &=1168. 6. Calculator of Mean And Standard Deviation for a Probability Distribution Instructions: You can use step-by-step calculator to get the mean (\mu) (μ) and standard deviation (\sigma) (σ) associated to a discrete probability distribution. b. c. Compute mean and variance of $X$. Geometric Distribution 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. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter $a$ and $b$. Let $X$ denote the number appear on the top of a die. Suppose $X$ denote the number appear on the top of a die. 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} 2. Find the probability that the last digit of the selected number is, eval(ez_write_tag([[728,90],'vrcacademy_com-large-mobile-banner-2','ezslot_13',121,'0','0']));a. The possible values of $X$ are $0,1,2,\cdots, 9$. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. b. The mean μ of a discrete random variable X is a number that indicates the … \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. 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. Let $X$ denote the last digit of randomly selected telephone number. 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 uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. To understand more about how we use cookies, or for information on how to change your cookie settings, please see our Privacy Policy. Find the value of $k$. \end{aligned} $$,$$ \begin{aligned} E(X^2) &=\sum_{x=0}^{5}x^2 \times P(X=x)\\ &= \sum_{x=0}^{5}x^2 \times\frac{1}{6}\\ &=\frac{1}{6}( 0^2+1^2+\cdots +5^2)\\ &= \frac{55}{6}\\ &=9.17. Let the random variable $Y=20X$. For variance, we need to calculate $E(X^2)$. 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. To analyze our traffic, we use basic Google Analytics implementation with anonymized data. The variance of discrete uniform distribution $X$ is, \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. This geometric probability calculator is used to find geometric distribution probability with total number of occurrence & probability … Uniform (Discrete) Distribution. \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. The calculator can also solve for the number of trials required. Determine mean and variance of Y. This list has either a finite number of members, or at most is countable. Step 4 - Click on âCalculateâ for discrete uniform distribution, Step 6 - Calculate cumulative probabilities. \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. As the given function is a probability mass function (pmf), 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} $$, Thus the probability mass function (pmf) of X is,$$ \begin{aligned} P(X=x) =\frac{1}{5}, x=4,5,6,7,8 \end{aligned} $$. Then the random variable X take the values X=1,2,3,4,5,6 and X follows U(1,6) distribution. A discrete random variable has a discrete uniform distribution if each value of the random variable is equally likely and the values of the random variable are uniformly distributed throughout some specified interval. Then the mean of discrete uniform distribution Y is,$$ \begin{aligned} E(Y) &=E(20X)\\ &=20\times E(X)\\ &=20 \times 2.5\\ &=50. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. So p ()1 =PM()=1= 1 3, p()2 = 1 2, p()3 = 1 6. Hope you like article on Discrete Uniform Distribution. \end{aligned} , Let Y=20X. \end{aligned},  \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=9.17-[2.5]^2\\ &=9.17-6.25\\ &=2.92. Suppose $X$ denote the last digit of selected telephone number.

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