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Let X be a discrete random variable with probability function 2 f(x) = P(X= z) = for z=1,2,3,... 3 (a) Find the cumulative distribution function of X. (b) Find P(X= 4+r | X > 4), z = 1,2,.... and compare the value with P(X= z). (e) Let R be the remainder when X is divided by 4. Find the probability function and t

Let X be a discrete random variable with probability function 2 f(x) = P(X= z) = for z=1,2,3,... 3 (a) Find the cumulative distribution function of X. (b) Find P(X= 4+r | X > 4), z = 1,2,.... and compare the value with P(X= z). (e) Let R be the remainder when X is divided by 4. Find the probability function and t

A First Course in Probability (10th Edition)
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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Let X be a discrete random variable with probability function f(x) = P(X = x) = 3²/12 for r=1,2,3,... (a) Find the cumulative distribution function of X. (b) Find P(X= 4+r | X > 4), r=1,2,.... and compare the value with P(X = z). (c) Let R be the remainder when X is divided by 4. Find the probability function and the cumulative distribution function for R. (d) Find E(R) and Var(R).
Transcribed Image Text:Let X be a discrete random variable with probability function f(x) = P(X = x) = 3²/12 for r=1,2,3,... (a) Find the cumulative distribution function of X. (b) Find P(X= 4+r | X > 4), r=1,2,.... and compare the value with P(X = z). (c) Let R be the remainder when X is divided by 4. Find the probability function and the cumulative distribution function for R. (d) Find E(R) and Var(R).
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