1/ Let X1 and X2 be two independent random variables each with probability density function

| August 30, 2017

uestion
1/ Let X1 and X2 be two independent random variables each with probability density function fXi(xi) = e-xi, for xi> 0 for i = 1,2.

(a) Find the joint probability density function of X1 and X2.

(b) Find P(X1 > 1, X2 < 1).

(c) Find P(X1 + X2 < 2).

2/ Let X be a continuous variable with probability density function

f(x) = kx(1 – x)2with 0 < x < 1, 0 otherwise.

(a) Find a value of k so that f(x) is a proper density.

(b) Find the cumulative distribution function of X.

(c) Find P(0.25 < X 0.5).

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