A continuous random variable is said to have a Rayleigh distribution with parameter if its PDF

A continuous random variable is said to have a Rayleigh distribution with parameter σ if its PDF is given by

where σ > 0.

a. If X ∼ Rayleigh(σ), find EX.

b. If X ∼ Rayleigh(σ), find the CDF of X,F_X(x).

c. If X ∼ Exponential(1) and Y = √2σ²X, show that Y ∼ Rayleigh(σ).

Transcribed Image Text:

X -x²/20² fx(x) e 02 -x²/20² {** 0 u(x) if x ≥ 0 if x < 0