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 distribution: no uses, 0.1; 1 use, 0.5; and 2 uses, 0.4. For example, 50% of the daily records show that the tool was used one time. Letting X denote the daily demand, find the following:

(i) E(X) and V(X).

(ii) If it costs the factory $10 each time the tool is used, find the mean and the variance of the daily costs of using this tool.

Solution

i)

Consider the table:          
          
x   P(x)   x P(x)   x^2 P(x)
0   0.1   0   0
1   0.5   0.5   0.5
2   0.4   0.8   1.6
          
Totals       1.3   2.1
       =E(x)   =E(x^2)
          
Thus,          
          
E(x) =    1.3       [ANSWER]

Var(x) = E(x^2) - E(x)^2 =    0.41   [ANSWER]  

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ii)

E(10x) = 10E(x) = $13 [answer]

V(10x) = 10V(x) = 10*0.41 = 4.1 [answer]