(b) Let X and Y have joint probability density function fxx (,)= k, x>0, y > 0, x+y<1 0, otherwise. (i) Show that k = 2. (ii) Find the marginal probability density functions of X and Y. (iii) Find the conditional probability density functions fxx (xly) and fy|x (y|x).

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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(b) Let X and Y have joint probability density function
fxx (2,3)=ô 0,2+y<1
0, otherwise.
(i) Show that k = 2.
(ii) Find the marginal probability density functions of X and Y.
(iii) Find the conditional probability density functions fxx (xly) and
fy|x (ylx).
(iv) Find the conditional expectation E(XY) and the conditional
variance var (XY).
(v) Find E (E (XY)). Hence verify the formula E (X) = E (E (X|Y)).
(vi) Are X and Y independent? Give reasons.
Transcribed Image Text:(b) Let X and Y have joint probability density function fxx (2,3)=ô 0,2+y<1 0, otherwise. (i) Show that k = 2. (ii) Find the marginal probability density functions of X and Y. (iii) Find the conditional probability density functions fxx (xly) and fy|x (ylx). (iv) Find the conditional expectation E(XY) and the conditional variance var (XY). (v) Find E (E (XY)). Hence verify the formula E (X) = E (E (X|Y)). (vi) Are X and Y independent? Give reasons.
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