申論題

1. (25%) If z follows a normal distribution, i.e., z~ND, its probability density and cumulative distribution functions are

and

respectively. If follows a bivariate normal distribution, ie,,

the corresponding probability density and cumulative distribution functions are and

respectively.

(b) (15%) Evaluate the expectation E[exp(x + y)I{x ≤ 0}], where I{A} is an indicator function returning 1 (0) ifthe condition A is true (false), and express the calculation result a +bn₁(c;0,1)+dN₁(e;0,1)+fn₁(g:0,1)n₁(h;0,1)+ in1(j；0,1)N₁(k;0,1)+ IN₂.What are a, b, c, d, e, f, g, h, i, j, k, I, m, and n?