Consider two random variables X and Y with joint PMF given in the following Table x= Number of Bars of Signal Strength 1 2 3 y= Response 1 0.01 0.02 0.25 time(nearest second) 2 0.02 0.03 0.20 3 0.02 0.10 0.05 4 0.15 0.10 0.05 a) Find P(X = 1, Y≤3) b) Find the marginal PMFs of X and Y. c) Find P(Y=1|X=1) d) Are X and Y independent? e) For the discrete random variables X and Y, Find E(Y|X=1) and V(Y|X=1)?

Consider two random variables X and Y with joint PMF given in the following Table x= Number of Bars of Signal Strength 1 2 3 y= Response 1 0.01 0.02 0.25 time(nearest second) 2 0.02 0.03 0.20 3 0.02 0.10 0.05 4 0.15 0.10 0.05 a) Find P(X = 1, Y≤3) b) Find the marginal PMFs of X and Y. c) Find P(Y=1|X=1) d) Are X and Y independent? e) For the discrete random variables X and Y, Find E(Y|X=1) and V(Y|X=1)?

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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