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1. The discrete random variables X and Y have known joint probability mass function [c x=0,1,2,L,9, y = 0, 1, 2,L,9, y≥x с where c = 1/55. 0 otherwise Py(x, y) given by Pxy(x, y) =< Define the event B = {X² +Y² ≤25}. a) Determine the conditional PMF P(x, y/B) of the random variables X and Y. b) Determine the conditional marginal PMFs P(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.) 2

1. The discrete random variables X and Y have known joint probability mass function [c x=0,1,2,L,9, y = 0, 1, 2,L,9, y≥x с where c = 1/55. 0 otherwise Py(x, y) given by Pxy(x, y) =< Define the event B = {X² +Y² ≤25}. a) Determine the conditional PMF P(x, y/B) of the random variables X and Y. b) Determine the conditional marginal PMFs P(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.) 2

A First Course in Probability (10th Edition)
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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soultions from previous is COV(x,y)=3, corraaltion = pxy=1/2, 

1. The discrete random variables X and Y have known joint probability mass function x = 0,1,2,L,9, y=0,1,2,L,9, y≥x otherwise where c = 1/55. Py(x, y) given by Pxy(x, y) = Define the event B = {X² +Y² ≤25}. a) Determine the conditional PMF P(x, y / B) of the random variables X and Y. b) Determine the conditional marginal PMFs Px(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.)
Transcribed Image Text:1. The discrete random variables X and Y have known joint probability mass function x = 0,1,2,L,9, y=0,1,2,L,9, y≥x otherwise where c = 1/55. Py(x, y) given by Pxy(x, y) = Define the event B = {X² +Y² ≤25}. a) Determine the conditional PMF P(x, y / B) of the random variables X and Y. b) Determine the conditional marginal PMFs Px(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.)
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