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Unformatted text preview: π/ 2 to π/ 2 as its argument goes from1 to 1. The deﬁnition of a function describes the domain as well as the rule. 2 3. [20 pts.] Suppose X is a random variable having PDF given by f ( x ) = 2 θ 2 ( θ + x ) 3 , < x < ∞ , where θ > 0 is a parameter. Find its distribution function (DF). Be sure to deﬁne the DF on the whole real line. 3 4. [20 pts.] Suppose the random vector ( X,Y ) has the PDF f ( x,y ) = 6(1 + x + y 2 ) 11 , < x < 1 , < y < 1 . (a) Find the conditional PDF of Y given X . (b) Find the conditional PDF of X given Y . 4 5. [20 pts.] Suppose the conditional distribution of Y given X is Exp( X ), and suppose the marginal distribution of X is Gam( α,λ ), where α > and λ > 0. What is the conditional distribution of X given Y ? Since this is a brand name distribution, no integrals need be done, it is enough to name the distribution and give its parameters as a function of Y , α , and λ . 5...
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 Fall '02
 Staff
 Probability theory

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