(a)

The function is and the interval is .

The probability density function: .

Substitute , and in the above integral.

Let , then .

Let , then .

Integration by parts: .

L-hospital rule

for all .

Since for all ,  probabilities are measured on a scale from to as .

Therefore, is a probability density function.

(b)

Find .

The integral form of above expression is .

.

(a) for all and .

(b) .