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]= 1
 
var[XY]= ???

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

P(XY≥1)= ???

Answer 1

please solve P(XY≥1)=

Answer 2

var(XY) = E[(XY)^2] - (E[XY]^2) = 7/9

Answer 3

please solve P(XY≥1)= 0.40343