Can anybody try to solve and explain these problems? Thanks!

The joint density of the random variables X and Y is ¼ in the square 0<x<2, 0<y<2. Let W=min(X, Y). Calculate E (W).

Answer: 2/3

A random variable X has the following CDF.

F(x)= x/2 0<x<1

1 x>(or equal to) 1

Let M(t) be the moment generating function of X. Calculate M(ln2).

Answer: 1/ln2+1

The joint density of the random variables X and Y is ¼ in the square 0<x<2, 0<y<2. Let W=min(X, Y). Calculate E (W).

Answer: 2/3

A random variable X has the following CDF.

F(x)= x/2 0<x<1

1 x>(or equal to) 1

Let M(t) be the moment generating function of X. Calculate M(ln2).

Answer: 1/ln2+1

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