Question 2 [6 marks] Consider the distribution Fs,t with the density function 1 -t Ps, t ( X ) = 21X(s+ tx) V ( b - x) (x - a), asxsb, with a = a(s, t) = (1 - h)2 (1 + h) 2 (1 - t) 2' b = b (s, t ) (1 - t) 2' h = h(s, t) =(s+t-st)1/2. [2] (a) Show that the first moment X Ps.t ( x) dx = 1 - t [2] (b) Show that the second moment x 2 Ps. ( x ) dx = h2 + 1 - t (1 - t) 3 [2] (c) Show that the variance equals h2/ (1 - t) 3