Question: A nonnegative function is called a probability density function if The probability that x lies between a and b is given by The expected

A nonnegative function ƒ is called a probability density function if

f(t) dt = 1.

The probability that x lies between a and b is given by 

The expected value of x is given by

In Exercises 

(a) Show that the nonnegative function is a probability density function

(b) Find P(0 ≤ x ≤ 4)

(c) Find E(x).

f(t) dt = 1.

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