~ 2. Let X Exponential(\ variable with PDF = = ½), let Y~ Uniform(a = 1, b = 3), and let Z be the random. fz(t) = {2/12 √2/t2 t≥1, t< 1. These have something in common: E[X] = E[Y] = E[Z] = 2. For each random variable, find the probability that it's less than this expected value. 3. Find the variance of each random variable in question 2.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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~
2. Let X Exponential(\
variable with PDF
=
= ½), let Y~ Uniform(a = 1, b = 3), and let Z be the random.
fz(t) =
{2/12
√2/t2 t≥1,
t< 1.
These have something in common: E[X] = E[Y] = E[Z] = 2. For each random variable, find
the probability that it's less than this expected value.
3. Find the variance of each random variable in question 2.
Transcribed Image Text:~ 2. Let X Exponential(\ variable with PDF = = ½), let Y~ Uniform(a = 1, b = 3), and let Z be the random. fz(t) = {2/12 √2/t2 t≥1, t< 1. These have something in common: E[X] = E[Y] = E[Z] = 2. For each random variable, find the probability that it's less than this expected value. 3. Find the variance of each random variable in question 2.
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