Let X N(,2). Let Y = eX. (Y is said to follow a lognormal distribution since log(Y ) = X which follows a normal distribution).

(a) Find the pdf of Y .

(b) FindE(Y) [Hint:] (i) It is easier to use the rule of the lazy statistician; (ii) Re-arrange the integrand inside the integral into a Normal pdf (with different mean and variance) and constant, and note that the integral of a pdf is always one.

(c) If 2 is small, find a normal distribution approximation for Y , using the delta method.