Expected Value of Random Variables

[Quincy]

Homework Statement

Consider a random variable X having cdf:

1, x ≥ 4,
3/4, 1 ≤ x < 4,
F_X(x) = 1/2, 0 ≤ x < 1,
1/4, −1 ≤ x < 0,
0, x < −1.

Give the value of E(X).

Homework Equations

The Attempt at a Solution

I know how to calculate the value of E(X) given the probability mass function (E(X) = x1*p(x1) + x2*p(x2) + ...) but how do I calculate E(X) given the cdf?

 

[vela]

You can find the probability density (what you are referring to as the probability mass function) from the cdf. Think about what the discontinuous jumps in the cdf represent.

 

[Quincy]

Hmm.. so would the pmf be:

0.25, x = -1
0.25, x = 0
0.25, x = 1
0.25, x = 4

?

 

[vela]

Yup!