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

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 42E
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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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