Question

A company plans a major investment and the

amount of profit is uncertain, but researchers
give the following estimate for the distribution.
1.5
10

Profit
(in
millions)
Probability

0.1
0.2
0.4
0.2
0.1
What is the expected value of the profit?
[ ? ] million dollars

Answer 1

3 million dollars

Explanation:

Given probability distribution table:

`\begin{array}c\cline{1-6} \text{Profit (in millions)} & 1 & 1.5 & 2 & 4 & 10\\\cline{1-6} \text{Probability} & 0.1 & 0.2 & 0.4 & 0.2 & 0.1\\\cline{1-6}\end{array}`

Expected Value formula:

`\displaystyle E(x)=\sum x_iP(x_i)`

where:

• 
  `x_i` = all possible values for the random variable

• 
  `P(x_i)` = respective theoretical probability

Let x = Profit (in millions)

Use the expected value formula to find the expected value:

`\begin{aligned}E(x) & = 1(0.1)+1.5(0.2)+2(0.4)+4(0.2)+10(0.1)\\& = 0.1 + 0.3+0.8+0.8+1\\& = 3\end{aligned}`

Therefore, the expected value of the profit is 3 million dollars.