The manager of a stockroom in a factory knows from his study

The manager of a stockroom in a factory knows from his study of records that the daily demand (number of times used) for a certain tool has the following probability

0.4

(a) Letting X denote the daily demand, find E(X) and V(X).

(b) Suppose that it cost the factory $10 each time the tool is used. Find the mean and the variance of the daily costs of using this tool.

Solution

0.4

So,

E(X) = 0 (0.1) + 1 (0.5) + 2(0.4)

= 1.3

V(X) = 0.1 * (0 - 1.3)² +  0.5 * (1 - 1.3)² +  0.4 * (2 - 1.3)²

= 0.41

b)

Mean of the cost:

E(X) = 0 (0.1) + 10 (0.5) + 20(0.4)

= 13

V(X)

=  0.1 * (0 - 13)² +  0.5 * (10 - 13)² +  0.4 * (20 - 13)²

= 41

Hope this helps.Ask if you have any doubts.