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Suppose that X 1 and X 2 are independent random variables and both have uniform distributions
on [ 0 , 1 ] . Find the distribution of X 1 X 2 . Suppose that X , Y and Z are independent random
variables each with a uniform distribution on [ 0 , 1 ] . Calculate P ( X + Y + Z < 1 ) .

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  • 1. Suppose that X 1 and X 2 are independent random variables and both have uniform distributions on [ 0 , 1 ] . Find the distribution of X 1 X 2 . Suppose that X , Y and Z are independent random variables each with a uniform distribution on [ 0 , 1 ] . Calculate P ( X + Y + Z < 1 ) .