- #1

Of Mike and Men

- 54

- 3

## Homework Statement

A small manufacturing firm sells 1 machine per month with 0.3 probability; it sells 2 machines per month with 0.1 probability; it never sells more than 2 machines per month. If X represents the number of machines sold per month and the monthly profit is 2X

^{2}+ 3X + 1 (in thousands of dollars), find the expected monthly profit.

## Homework Equations

## The Attempt at a Solution

E(2X

^{2}+ 3X + 1) = ∑(2X

^{2}+ 3X + 1)f(x), x = 1, 2

= (2+3+1)(.3) + (8+6+1)(.1)

= 1.8 + 1.5

= 3.3

3.3 * 1000 = $3,300

The answer in the back is $3,800.

If I take my 3.3 and add the mean of E(X) = .3(1) + 2(.1) = 0.5, I get 3.8 * 1000 = $3,800. I'm not sure if this is coincidence or actually how you solve the problem. If it's how you solve the problem, I don't understand why you add the mean of X. If it's not the way you solve it, I'm not sure what to do and would like some hints (but not a solution -- if possible) as to where to go.

Thanks.