Change of variables: Let = g(), where g is a monotone function of , and let h be the inverse of g so that

Change of variables: Let ψ = g(θ), where g is a monotone function of θ, and let h be the inverse of g so that θψ = h(ψ). If p _θ (θ) is the probability density of θ, then the probability density of ψ induced by Po is given by P _ψ (ψ) = P _θ (h(ψ)) x |dh/dψ|

(a) Let θ ∼ beta(a, b) and let ψ = log[θ/(1 – θ)]. Obtain the form of p _ψ and plot it for the case that a = b = 1.

(b) Let θ ∼ gamma (a, b) and let ψ = log θ. Obtain the form of p _ψ and plot it for the case that a = b =1.