2 Let be a fixed positive constant and define the function f

2. Let be a fixed positive constant, and define the function f(x) by f(x) = (1/2)(lambda)e^(-lambda*x) if x>0 and  f(x) = (1/2)(lambda)e^(lambda*x) if x<0.

(a) Verify that f(x) is a pdf.

(b) If X is a random variable with pdf given by f(x), find P(X < t) for all t.

Evaluate all integrals.

(c) Find P(|X| < t) for all t. Evaluate all integrals

Solution