Exercise 5.3 For an exponentially distributed random variable X Exp(), let (x) = x. Show that E[(X)] = 1 and the transformation (5.7) defines

Exercise 5.3 For an exponentially distributed random variable X ∼ Exp(λ), let λ(x) = λx. Show that E[λ(X)] = 1 and the transformation (5.7) defines an Erlang distribution of order 2; see (3.25). How about the case that λ(x) = x/n for X ∼ χ2 n, the chi-square distribution.