Question: Problem 1 [My generation] (30 pts) Let X1 ~ Unif[0, 1] and X2 ~ Unif[0, 1] be independent, uniform random variables on [0, 1]. Let

Problem 1 [My generation] (30 pts) Let X1 ~ Unif[0, 1] and X2 ~ Unif[0, 1] be independent, uniform random variables on [0, 1]. Let Y = X1 + X2. (a) (10 points) Determine and sketch precisely the pdf fy (y) and cdf Fy (y) of the ran- dom variable Y. Give explicit mathematical formulas for both fy(y) and Fy(y). (b) (20 points) Find a function g(x) such that Y = g(X1). Give an explicit mathematical formula for g(x)

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