# Thread: Multiplying independent random variables

1. ## Multiplying independent random variables

If iv got independent random variables Y1 ~ LN(1, $v^2$) and Y2 ~ LN(2, 2 $v^2$)....

am i right in thinking that X=Y1+Y2 has distribution LN(3, 3 $v^2$)?

How do i find the distribution of W=Y1Y2?

2. Originally Posted by sirellwood
If iv got independent random variables Y1 ~ LN(1, $v^2$) and Y2 ~ LN(2, 2 $v^2$)....

am i right in thinking that X=Y1+Y2 has distribution LN(3, 3 $v^2$)?

How do i find the distribution of W=Y1Y2?
Theorem: If X and Y are two independent and continuous random variables with pdf’s f(x) and g(y) respectively, then the sum U = X + Y is a continuous random variable with pdf given by $\displaystyle h(u) = \int_{-\infty}^{+\infty} f(u - y) \, g(y) \, dy$.

Theorem: If X and Y are two independent and continuous random variables with pdf’s f(x) and g(y) respectively and Pr(X = 0) = Pr(Y = 0) = 0, then the product U = XY is a continuous random variable with pdf given by $\displaystyle h(u) = \int_{-\infty}^{+\infty} \frac{1}{|y|} \, f \left(\frac{u}{y}\right) \, g(y) \, dy$.