Homework SourseA chemical supply company currently has in stock 100 lb of a
A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 8-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that Xhas the following pmf.
Compute E(X) and V(X).
Compute the expected number of pounds left after the next customer\'s order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.]
| x | 1 | 2 | 3 | 4 |
| p(x) | 0.2 | 0.5 | 0.2 | 0.1 |
Solution
Q1.
f= 1
fx = 2.2
Mean = fx / f = 2.2
Mean square = f x^2 / f = 5.6
Varriance = (Mean square) - (Mean)^2
Varriance = f x^2 - Mean^2 = 0.76
Stadard Dev= Var = 0.872
E(X) = 2.2, V(X) = 0.76
| Values ( X ) | Frequency(f) | fx | ( X^2) | f x^2 |
| 1 | 0.2 | 0.2 | 1 | 0.2 |
| 2 | 0.5 | 1 | 4 | 2 |
| 3 | 0.2 | 0.6 | 9 | 1.8 |
| 4 | 0.1 | 0.4 | 16 | 1.6 |
