Homework SourseA store manager estimates that in two years a computer with
A store manager estimates that in two years a computer with 16 GB RAM will sell with probability 0.6, a computer with 8 GB RAM will sell with a probability 0.3, and a computer with 4 GB RAM will sell with probability 0.1. The profits associated with the sales in that year are estimated to be $60 million, $20 million, and $10 million, respectively. Let X be the total profit of computers during that year.
a) Determine the probability mass function of X.
b) Determine the cumulative distribution function of X.
c) Determine the mean and variance of X.
Solution
X -- Profit of computers during that year
| Computer | 16Gb | 8gb | 4gb | Total |
| Prob(PDF x) | 0.6 | 0.3 | 0.1 | 1 |
| Profit X | 60 | 20 | 10 | 90 |
| x*p | 36 | 6 | 1 | 43 |
| x^2 p | 2160 | 120 | 10 | 2290 |
| Mean | 43 | million | ||
| Variance | 2290-43^2 | million | ||
| Variance | 441 |
