Q 3. (a) If the joint probability density function of X and Y is given by | 24:ry for 0 < r < 1,0 < y < 1, r + y < 1 S (x, y) = clsewhere find (i) P(X +Y < ), (ii) conditional expectation, E (X |Y = y), and (iii) conditional variance, Var (X |Y = y). (b) Suppose that X is a standard normal random variable. Show that Y variable with one degree of freedom by showing that its probability density function is X² is a chi-squared random 1 1 2 VT f (y) = ; y> 0.
Q 3. (a) If the joint probability density function of X and Y is given by | 24:ry for 0 < r < 1,0 < y < 1, r + y < 1 S (x, y) = clsewhere find (i) P(X +Y < ), (ii) conditional expectation, E (X |Y = y), and (iii) conditional variance, Var (X |Y = y). (b) Suppose that X is a standard normal random variable. Show that Y variable with one degree of freedom by showing that its probability density function is X² is a chi-squared random 1 1 2 VT f (y) = ; y> 0.
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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