Let X be a continuous r.v. with CDF F and PDF f. (a) Find the conditional CDF of X given

Chapter 5, Problem 4

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Let X be a continuous r.v. with CDF F and PDF f. (a) Find the conditional CDF of X given X>a (where a is a constant with P(X > a) 6= 0). That is, find P(X x|X>a) for all a, in terms of F. (b) Find the conditional PDF of X given X>a (this is the derivative of the conditional CDF). (c) Check that the conditional PDF from (b) is a valid PDF, by showing directly that it is nonnegative and integrates to 1.

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