# Question: The positive random variable X is said to be a

The positive random variable X is said to be a lognormal random variable with parameters μ and σ2 if log(X) is a normal random variable with mean μ and variance σ2. Use the normal moment generating function to find the mean and variance of a lognormal random variable.

## Answer to relevant Questions

Let A1, A2, . . . ,An be arbitrary events, and define Ck = {at least k of the Ai occur}. Show that Let X denote the number of the Ai that occur. Show that both sides of the preceding equation are equal to E[X]. We say that X is stochastically larger than Y, written X ≥st Y, if, for all t. P{X > t} ≥ P{Y > t} Show that if X ≥st Y, then E[X] ≥ E[Y] when (a) X and Y are nonnegative random variables; (b) X and Y are arbitrary ...Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a deuce, or the 3rd a three, or . . ., or the 13th a king, or the 14 an ace, and so on, we say that a ...If X1, X2, . . . ,Xn are independent and identically distributed random variables having uniform distributions over (0, 1), find (a) E[max(X1, . . . ,Xn)]; (b) E[min(X1, . . . ,Xn)]. If 10 married couples are randomly seated at a round table, compute (a) The expected number and (b) The variance of the number of wives who are seated next to their husbands.Post your question