# Expected values

• March 11th 2006, 04:53 PM
Kiwigirl
Expected values
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. • March 12th 2006, 03:32 AM rgep 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 $b=-900$. • March 12th 2006, 03:36 AM CaptainBlack Quote: 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.

$
\mathrm{Var}(prof)=\frac{1}{n}\sum_{i=1}^n (prof_i-\overline{prof})^2\ p(prof_i)
$

$
=(375-900-225)^2 0.1+(2\times375-900-225)^2 0.2+$
$(3\times375-900-225)^2 0.3+(4\times375-900-225)^2 0.4
$

$
=140625
$

Quote:

b) Find the standard deviation in profit each week.
Standard deviation is the square root of variance and so:

$
\sigma=\sqrt{140625}=\375
$

RonL