Let X and Y be independent random variables, each uniformly distributed on the interval [0,2].

Question

Find the mean and variance of XY.

E[XY]=
 
var[XY]=

Find the probability that XY≥1. Enter a numerical answer.

P(XY≥1)=

Answer 1

E[XY] = 1
var[XY] = 7/9
p(XY >= 1) = ??

Answer 2

p(XY >= 1) = 2/5

Answer 3

p(XY >= 1) = 0.40343