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Z N(0, 1) and (z) is its CDF. Let X N( = 3, 2 = 9). (1) if (1.96) = 0.975. Find x* such that

Z N(0, 1) and (z) is its CDF. Let X N( = 3, 2 = 9).

(1) if (1.96) = 0.975. Find x* such that P(X x* ) = 0.025.

(2)Let U = 3X + 1. prove that U has a normal distribution by deriving its MGF.

(3) there is a transformed variable Y = e 1+2X. Find its expected value E(Y ).

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