Let f 1|2 (x 1 |x 2 ) = c 1 x 1 /x 2 2 ,
Question:
Let f1|2(x1|x2) = c1x1/x22 , 0 < x1 < x2, 0 < x2 < 1, zero elsewhere, and f2(x2) = c2x42 , 0 < x2 < 1, zero elsewhere, denote, respectively, the conditional pdf of X1, given X2 = x2, and the marginal pdf of X2. Determine:
(a) The constants c1 and c2.
(b) The joint pdf of X1 and X2.
(c) P(1/4 < X1 < 1/2|X2 = 5/8).
(d) P(1/4 < X1 < 1/2).
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Step by Step Answer:
a c1 lnx1x2 lnx2 c2 lnx2 x22lnx1 For b we have for all x1 x2 0 f12x1x2 c1c12lnx1x22 lnx22c12c1...View the full answer
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Related Book For 
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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