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Find E(Y|X=1).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The joint distribution of X and Y is given in the following table . X = 0 X = 1 X = 3 Y=-1 0.11 0.03 0.00 Y=2.5 0.03 0.09 0.16 Y=3 0.15 0.15 0.06 Y=4.7 0.04 0.16 0.02 Find E(Y|X=1). Give answer up to three decimal place.
Transcribed Image Text:The joint distribution of X and Y is given in the following table . X = 0 X = 1 X = 3 Y=-1 0.11 0.03 0.00 Y=2.5 0.03 0.09 0.16 Y=3 0.15 0.15 0.06 Y=4.7 0.04 0.16 0.02 Find E(Y|X=1). Give answer up to three decimal place.
X ) for 1<x<2, 0<y<1 4 Consider two continuous random variables X and Y with joint pdf f(x,y)= k(2y- (a) What must the value of k be for this to be a valid pdf? Answer to two significant figures. (b)Derive the marginal pdf of X and use it to compute E(X). What is E(X)? 13 O k(- - ) 10 11 k - 12 O k 11 10 k (- 13 (c)Derive the marginal pdf of Y and use it to compute E(Y ). What is E(Y )? 20 k (- -) 35 35 k(- 20 23 k 48 48 k(- 23 (d) Derive the conditional pdf of Y given X = x and use it to compute E(Y |X = 1.2); note that the answer does not depend on k. What is E(Y |X 1.2)? Answer to four significant figures. (e)Are X and Y independent? Yes No
Transcribed Image Text:X ) for 1<x<2, 0<y<1 4 Consider two continuous random variables X and Y with joint pdf f(x,y)= k(2y- (a) What must the value of k be for this to be a valid pdf? Answer to two significant figures. (b)Derive the marginal pdf of X and use it to compute E(X). What is E(X)? 13 O k(- - ) 10 11 k - 12 O k 11 10 k (- 13 (c)Derive the marginal pdf of Y and use it to compute E(Y ). What is E(Y )? 20 k (- -) 35 35 k(- 20 23 k 48 48 k(- 23 (d) Derive the conditional pdf of Y given X = x and use it to compute E(Y |X = 1.2); note that the answer does not depend on k. What is E(Y |X 1.2)? Answer to four significant figures. (e)Are X and Y independent? Yes No
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