5.23 Let 2 r () be a 2 random variable with r degrees of freedom and noncentrality parameter . (a) Show that E 1 2

5.23 Let χ2 r (λ) be a χ2 random variable with r degrees of freedom and noncentrality parameter λ.

(a) Show that E 1

χ2 r (λ) = E 1

E 1

χ2 r+2K

|K 2

= E 1 r−2+2K

!

, where K ∼

Poisson(λ/2).

(b) Establish (5.32).