1. Random variables X and Y have joint PDFfx,y(x, y) = { cry“ 0Y} and Pr{Y < X²}.c) Find Pr{min(X,Y) < 1/2}.d) Find Pr{max(X,Y)< 3/4}.2. Random variables X and Y have joint PDFfx.x(x, y) = {|cx 0

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1. Random variables X andY have joint PDF fx,Y (x, y) = { cry 0Y} and Pr{Y < X²}. c) Find Pr{min(X,Y) < 1/2}. d) Find Pr{max(X,Y) < 3/4}.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

1. Random variables X and Y have joint PDF
fx,y(x, y) = { cry“ 0<x<1,0 < y < 1
otherwise
a) Find the constant c.
b) Find Pr{X >Y} and Pr{Y < X²}.
c) Find Pr{min(X,Y) < 1/2}.
d) Find Pr{max(X,Y)< 3/4}.
2. Random variables X and Y have joint PDF
fx.x(x, y) = {|
cx 0<x < 1,0 < y < 1
otherwise
%3D
a) Find the constant c.
b) Find the marginal PDF fx(x).
c) Are X andY independent? Justify your answer.
3. Random variables X and Y have joint PDF
fx.y(x, y) = { day 0<x<1,0< y <1
otherwise
a) What are E[X] and Var[X]?
b) What are E[Y] and Var[Y]?
c) What is Cov[X,Y]?
d) What is E[X +Y] ?
e) What is Var[X +Y] ?
4. If X has an exponential (A) PDF, what is the PDF of W = X² ?
5. X and Y have joint PDF
fxx(x, y) = {
S (x +y)/3 0< x < 1,0 < y < 2,
otherwise
Let A = {Y < 1}.
a) What is Pr{A} ?
b) Find fx.y|a(x, y).
c) Find fx|a(x) and fy|a(y).

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