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Let X be a discrete random variable with probability function f(x) = P(X= x) = (1-p)p-2 for x = 2, 3, 4, 5, .... for some 0 < p < 1. (a) Find P(X> 4). (b) Find P(X=3+x | X > 4) for x = 2, 3, 4.... and compare this with P(X = x). (c) Let R be the remainder when X is divided by 5 (so R is a random variable taking possible values

Let X be a discrete random variable with probability function f(x) = P(X= x) = (1-p)p-2 for x = 2, 3, 4, 5, .... for some 0 < p < 1. (a) Find P(X> 4). (b) Find P(X=3+x | X > 4) for x = 2, 3, 4.... and compare this with P(X = x). (c) Let R be the remainder when X is divided by 5 (so R is a random variable taking possible values

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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2. Let X be a discrete random variable with probability function f(x) = P(X=x) = (1-p) p²-2 for x = = 2, 3, 4, 5,... for some 0 < p < 1. (a) Find P(X> 4). (b) Find P(X=3+x | X > 4) for x = 2,3,4.... and compare this with P(X = x). (c) Let R be the remainder when X is divided by 5 (so R. is a random variable taking possible values 0 or 1,2,3,4). Find the probability function and the cumulative distribution function for R. (d) Find the Expected Value E(R) and the variance Var (R) in the case p = = 1/2.
Transcribed Image Text:2. Let X be a discrete random variable with probability function f(x) = P(X=x) = (1-p) p²-2 for x = = 2, 3, 4, 5,... for some 0 < p < 1. (a) Find P(X> 4). (b) Find P(X=3+x | X > 4) for x = 2,3,4.... and compare this with P(X = x). (c) Let R be the remainder when X is divided by 5 (so R. is a random variable taking possible values 0 or 1,2,3,4). Find the probability function and the cumulative distribution function for R. (d) Find the Expected Value E(R) and the variance Var (R) in the case p = = 1/2.
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