Problem 1E

Let Y be a random variable with probability density function given by

Solution :

Step 1 of 5:

Let Y be a random variable with probability density function is given by

Our goal is:

a). We need to find the density function of .

b). We need to find the density function of .

c). We need to find .

d). We need to find E(), E() and E().

e). We need to find E(), E() and E() by the methods of chapter 4.

a).

Now we have to find the density function of .

Then we have to find .

=

=

=

Then the distribution function of is

.

And the density function of is