Suppose that X1 and X2 are independent random variables with

Suppose that X₁ and X₂ are independent random variables with E(X₁) = 2, E(X₂) = 5, V(X₁) = 2, V(X₂) = 10.

Define Y = X₁ x X₂

A) Compute the mean and variance of Y by propagation of error

B) If X₁ and X₂ are both distributed lognormal, what is the distribution of Y.... Give short explanation

Hints: For the distribution, choose one from Normal, Lognormal, Exponential, and Weibull.
Think about the natural logarithm of Y.

Solution