Page 109 - Schaum's Outlines - Probability, Random Variables And Random Processes
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MULTIPLE RANDOM VARIABLES [CHAP 3
Thus k = 1/zR2.
(b) By Eq. (3.30), the marginal pdf of X is
Hence
By symmetry, the marginal pdf of Y is
(c) For 0 5 a 5 R,
I- P
3.22. The joint pdf of a bivariate r.v. (X, Y) is given by
ke-(ax+by) x>O,y>O
otherwise
where a and b are positive constants and k is a constant.
(a) Determine the value of k.
(b) Are X and Y independent?
Thus k = ab.
(b) By Eq. (3.30), the marginal pdf of X is
By Eq. (3.31), the marginal pdf of Y is
Since fXy(x, y) = fx(x) fr(y), X and Y are independent.
