The profit from a firm’s operation can be $1 million, $4 million, $6 million, or $10...
The profit from a firm’s operation can be $1 million, $4 million, $6 million, or $10 million with probabilities 0.1, 0.3, 0.5, and 0.2, respectively. What is the variance for the firm’s profit?
Homework Answers
| x | P(x) | xP(x) | x2P(x) |
| 1 | 0.1000 | 0.1000 | 0.1000 |
| 4 | 0.3000 | 1.2000 | 4.8000 |
| 6 | 0.5000 | 3.0000 | 18.0000 |
| 10 | 0.2000 | 2.0000 | 20.0000 |
| total | 6.3000 | 42.9000 | |
| E(x) =μ= | ΣxP(x) = | 6.3000 | |
| E(x2) = | Σx2P(x) = | 42.9000 | |
| Var(x)=σ2 = | E(x2)-(E(x))2= | 3.2100 |
from above: variance for the firm’s profit =$ 3.21 million
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