Homework SourseSuppose that the probability mass function of a discrete ran
Suppose that the probability mass function of a discrete random variable X is given by the following table:
A) Compute EX.
B) Compute var(X). (Recall: var(X)=EX2.u2.)
| X | P(X=x) |
|---|---|
| -5 | 0.3 |
| -1 | 0.25 |
| 1 | 0.05 |
| 4 | 0.4 |
Solution
Let us calculate E(x) and E(x^2) first from the given data
From the above find that
E(x) = sum of x p(x) = -0.1
Var(x) = E(x^2) - Mean^2 = 14.2-(-0.1)2 = 14.2-0.01 = 14.19
| X | P(X=x) | xp(x) | x^2p(x) |
| -5 | 0.3 | -1.5 | 7.5 |
| -1 | 0.25 | -0.25 | 0.25 |
| 1 | 0.05 | 0.05 | 0.05 |
| 4 | 0.4 | 1.6 | 6.4 |
| -0.1 | 14.2 |
