# Question

A random variable has a CDF given by Fx (x) = (1 –e –z) u (x).

(a) Find Pr (X > 3).

(b) Find Pr (X < 5| X > 3).

(c) Find Pr (X > 6 | X > 3).

(d) Find Pr (|X –5| < 4||X –6| > 2).

(a) Find Pr (X > 3).

(b) Find Pr (X < 5| X > 3).

(c) Find Pr (X > 6 | X > 3).

(d) Find Pr (|X –5| < 4||X –6| > 2).

## Answer to relevant Questions

A random variable has a CDF given by (a) Find Pr (X =0) and Pr (X=1). (b) Find Pr(X 1/2). (c) Find Pr(X > 1/2|X >0). Suppose X is an exponential random variable with PDF, fX (x) = exp (– x) u (x). Find a transformation, Y= g(X) so that the new random variable Y has a Cauchy PDF given by A Cauchy random variable has a PDF (a) Find the characteristic function, ϕX(ω) . (b) Show that the derivatives dk / dωk (ϕX(ω)) do not exist at ω = 0.What does this mean? A certain random variable has a probability- generating function given by Find the PMF for this random variable. Prove the following properties of moment- generating functions. (a) MX (0) = 1. (b) For a nonnegative random variable X, and for real u < 0, MX (u) ≤ 1.Post your question

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