Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables with common density function f(x). (a) Compute P(X1 > X2) (b) Compute P(X1 > X2| X1 > X3) (c) Compute P(X1 > X2| X1 < X2)

Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables with common density function f(x). (a) Compute P(X1 > X2) (b) Compute P(X1 > X2| X1 > X3) (c) Compute P(X1 > X2| X1 < X2)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 13EQ

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Question

Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables
with common density function f(x).
(a) Compute P(X1 > X2)
(b) Compute P(X1 > X2j X1 > X3)
(c) Compute P(X1 > X2| X1 < X2)
Hint: You can answer this problem easily using symmetry.

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The joint probability mass function of XX and YY is given by p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1 Compute the following probabilities:P(X+Y>3)=P(X+Y>3)=P(XY=2)=P(XY=2)=P(XY>1)=P(XY>1)=