# Question: Let X be a normal random variable with mean

Let X be a normal random variable with mean μ and variance σ2. Use the results of Theoretical Exercise 46 to show that

In the preceding equation, [n/2] is the largest integer less than or equal to n/2. Check your answer by letting n = 1 and n = 2.

In the preceding equation, [n/2] is the largest integer less than or equal to n/2. Check your answer by letting n = 1 and n = 2.

## Answer to relevant Questions

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 ...In the text, we noted that when the Xi are all nonnegative random variables. Since an integral is a limit of sums, one might expect that whenever X(t), 0 ≤ t < ∞, are all nonnegative random variables; and this result is ...A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make n guesses sequentially, where the ith one is a guess of the card in ...Let X1, X2, . . . be a sequence of independent and identically distributed continuous random variables. Let N ≥ 2 be such that X1 ≥ X2 ≥ . . . ≥ XN−1 < XN That is, N is the point at which the sequence stops ...If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)2]; (b) Var(4 + 3X).Post your question