Let X N(,2). Show that (a) Z = (X) is N(0,1). (b) U = (X)2 2 is 2(1).

Let X ∼ N(μ,σ2). Show that (a) Z = (X−μ) σ is N(0,1). (b) U = (X−μ)2 σ2 is χ2(1).