This problem involves two continuous random variables X and Y with joint pdf given by J6x, x, y ≥ 0 and x+y≤1 fx,y(x, y) = 0, otherwise. That is, over the shaded region below, we have fx,y(x, y) = 6x. y (0,1) x (1,0) We can check that this is a valid joint pdf by integrating over the shaded region: .1 [ƒx,y (x, y) dx dy = [[ 6x dx dy = 1. (a) Let A denote the event {X <0.5}. Find the conditional pdf fx|A(x). (b) What is P(X + Y ≤ 1)? (c) What is P(X + Y ≤ 0.5)? (d) Let Z=XY. Find fz(z), the pdf of Z. Hint 1: X and Y are not independent. Hint 2: start by finding the cdf of Z.

This problem involves two continuous random variables X and Y with joint pdf given by J6x, x, y ≥ 0 and x+y≤1 fx,y(x, y) = 0, otherwise. That is, over the shaded region below, we have fx,y(x, y) = 6x. y (0,1) x (1,0) We can check that this is a valid joint pdf by integrating over the shaded region: .1 [ƒx,y (x, y) dx dy = [[ 6x dx dy = 1. (a) Let A denote the event {X <0.5}. Find the conditional pdf fx|A(x). (b) What is P(X + Y ≤ 1)? (c) What is P(X + Y ≤ 0.5)? (d) Let Z=XY. Find fz(z), the pdf of Z. Hint 1: X and Y are not independent. Hint 2: start by finding the cdf of Z.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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