Let A be a fixed positive constant, and define the function f(x) by f(x) = 1/2 e-

Question:

Let A be a fixed positive constant, and define the function f(x) by f(x) = 1/2 λe- λx if x > 0 and f(x) = 1/2 λeλx if x < 0.
(a) Verify that f(x) is a pdf.
(b) If A" is a random variable with pdf given by /(x), find P(X < t) for all t. Evaluate all integrals.
(c) Find P(|X| < t) for all t. Evaluate all integrals.