The system of the random variables (ξ, η) obeys the distributive law with the density function fξη(x, y). To find a density function fζ (z) for the random variable ζ = ξη. I n s t r u c t i o n . We...

The system of the random variables (ξ, η) obeys the distributive law with the density function fξη(x, y). To find a density function fζ (z) for the random variable ζ = ξη.

I n s t r u c t i o n . We fix some value z, then on a plane x0y we build a curve with an equation z = xy. It is a hyperbola. Distribution function is given by the formula

To find a distributive law of a random variable ζ = ξ + η, if ξ and η are independent random variables, which obey the exponential law with density functions