Find the probability density function of Y = eX when X is normally distributed with parameters μ and σ2. The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with parameters μ and σ2.
Answer to relevant QuestionsProve Corollary 2.1. An ambulance travels back and forth at a constant speed along a road of length L. At a certain moment of time, an accident occurs at a point uniformly distributed on the road. [That is, the distance of the point from one of ...Let f (x, y) = 24xy 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and let it equal 0 otherwise. (a) Show that f (x, y) is a joint probability density function. (b) Find E[X]. (c) Find E[Y]. In Problem 2, suppose that the white balls are numbered, and let Yi equal 1 if the ith white ball is selected and 0 otherwise. Find the joint probability mass function of (a) Y1, Y2; (b) Y1, Y2, Y3. Problem 2 Suppose that 3 ...The joint density function of X and Y is given by f (x, y) = xe−x(y+1) x > 0, y > 0 (a) Find the conditional density of X, given Y = y, and that of Y, given X = x. (b) Find the density function of Z = XY.
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