Question

1. A random variable \( X \) has the PDF given by: \[ f_{x}(x)=c e^{-2 x}, \quad x \geq 0 \] a. Compute the value of the constant \( C \) such that \( f_{x}(x) \) is a valid PDF b.

Answer 1

c = 2

Explanation:

We must have the area under the PDF to be 1.

=> int[ce^(-2x)]dx from x = 0 to x = ∞

= [-(c/2)e^(-2x)] from x = 0 to x = ∞

= (c/2) = 1. => c = 2.