Expected values

**Kiwigirl** · March 11th 2006, 03:53 PM

Silica Tech sell Hercules P150 desktop computer for $2400 (includes GST). The owner has kept a record of the number of computers, n, sold per week and the results are shown in this probability distribution (This is a table, but I don't know how to create a table on a thread, I think you will get the idea):

N............1......2......3.....4
P(N = n).. 0.1...0.2...0.3...0.4

The expected sales each week:
1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4 = 3.

The calculated variance of the sales each week = 1.

The fixed costs of the business (salaries, rent, power and so on) are $900 per week and the profit per computer is $375.

So, the expected profit each week:
375 (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) - 900 = 225.

a) Find the variance in profit each week.

b) Find the standard deviation in profit each week.

**rgep** · March 12th 2006, 02:32 AM

If $X$ is a random variable with variance $\sigma^2$ then the variance of $aX+b$ , for constants $a, b$ is $a^2\sigma^2$ . In your case $a=375$ and $b=-900$ .

**CaptainBlack** · March 12th 2006, 02:36 AM

Originally Posted by Kiwigirl

Silica Tech sell Hercules P150 desktop computer for $2400 (includes GST). The owner has kept a record of the number of computers, n, sold per week and the results are shown in this probability distribution (This is a table, but I don't know how to create a table on a thread, I think you will get the idea):

N............1......2......3.....4
P(N = n).. 0.1...0.2...0.3...0.4

The expected sales each week:
1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4 = 3.

The calculated variance of the sales each week = 1.

The fixed costs of the business (salaries, rent, power and so on) are $900 per week and the profit per computer is $375.

So, the expected profit each week:
375 (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) - 900 = 225.

a) Find the variance in profit each week.