Question

On the basis of his sale records, a salesman knows that his weekly commissions have the probabilities shown below.

Commission	0	$1,000	$2,000	$3,000	$4,000
Probability	0.14	0.2	0.46	0.1	0.1

Find the salesman's expected commission.
$

Answer 1

x	P(x)	x * P(x)
0$	0.14	0.000
1000$	0.2	200.000
2000$	0.46	920.000
3000$	0.1	300.000
4000$	0.1	400.000
∑xi = 10000.000	∑ P(xi) = 1.000	∑ xi*P(xi) = 1820.000$

The expected value E(X), or mean μX of a discrete random variable X

E(X) = μX = ∑ [ xi * P(xi) ]

E(X) = 0 * 0.14 + 1000 * 0.2 + 2000 * 0.46 + 3000 * 0.1 + 4000 * 0.1

E(X) = 0.000 + 200.000 + 920.000 + 300.000 + 400.000 = 1820.000%

E(X) = 1820.000$

therefore expected sales'man commision =1820.000$