An engineering firm bids on contracts for the short-term jobs where each job can generate the profit of $100,000 for the firm. Assume the probabilities of getting zero to five such jobs in the certain month are given in table below:
| Number of jobs |
Probability |
| 0 |
0.05 |
| 1 |
0.15 |
| 2 |
0.20 |
| 3 |
0.25 |
| 4 |
0.20 |
| 5 |
0.15 |
a) Find out the expected profit throughout the month for firm.
b) Find out the variance of firm's profit for month.