Let X ∼ X ∼ Exponential ( λ λ ), and Y = aX Y = a X , where a a is a positive real number. Show that Y ∼ Y ∼ Exponential ( λ a λ a ).
The cumulative distribution function (cdf) of any random variable X is the function F X:R→ [0,1] F X: R → [ 0, 1] defined by