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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6f0fc2b-ed06-42f6-aea2-7d26d8b1334d%2Fc1e669fe-f0bd-4a9a-bcfc-3fecb0935a29%2Fia4l9fd_processed.png&w=3840&q=75)
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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