Suppose that two random variables Y1 and Y2 are independent, that is, for all values of y1 and y2,P((Yı = y1) n (Y2 = y2)) = P(Y1 = y1)P(Y2 = 42)that is, the events (Y1 = y1) and (Y2 = y2) are independent. Suppose also that Y1 and Y2 have thesame Geometric distribution, that is Y1 - Geometric(p) and Ý, - Geometric(p). Define a thirdrandom variable Y as the sum of Y and Y2, that is, Y = Y1 +Y2. By considering the Theorem of Total Probability and the partitioning resulty-1(Y = y) = U ((Yı = t) n (Y2 = y – t))t=1for y = 2,3, ..., derive the pmf of Y.

Answered: Image /qna-images/answer/740ddf41-ddb9-4693-b3ea-02ce6fa45978.jpg

Answered: Suppose that two random variables Y1…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The random variable X takes values -1, 0, 1 with probabilities 1/8, 3/8, 4/8 respectively. a) Write the CDF of X. b) Write the PMF of Y = X² + 2. %3D c) Compute E(Y).
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Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
5. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lq, Wq, c and utilization ratio.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lg, Wq, c and utilization ratio.
Given the joint probabilities of two discrete random variables (X, Y) as below.f(1,1)=4/20, f(1,2)= 3/20, f(1,3)= 1/20, f(2,1)= 2/20, f(2,2)=1/20, f(2,3)= 2/20, f(3,1)= 2/20, f(3,1)=3/20, f(3,3)= 2/20 . Find. i) The mean of a random variable Xii) The variance of random variable X.

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