# Expectations question

• January 13th 2006, 11:42 AM
fobster
Expectations question
This has something to do with expectations and its properties.

The sales per day for a product is estimated as follows based on past records

Daily demand (X) / Probaility

10 / .1
11 / .2
12 / .4
13 / .3

a. Obtain the mean and variance of the daily sales.
b. If the porfit can be described by the equation, profit= -10+(4*X)

What is the expected daily profit? What is the variance of the daily profit?
• January 13th 2006, 12:06 PM
CaptainBlack
Quote:

Originally Posted by fobster
This has something to do with expectations and its properties.

The sales per day for a product is estimated as follows based on past records

Daily demand (X) / Probaility

10 / .1
11 / .2
12 / .4
13 / .3

a. Obtain the mean and variance of the daily sales.
b. If the porfit can be described by the equation, profit= -10+(4*X)

What is the expected daily profit? What is the variance of the daily profit?

mean: $\mu = \sum_i$ $x_i.p(x_i) = (10\times 0.1)+(11 \times 0.2)+(12\times 0.4)+(13\times 0.3)$

variance: $\sigma^2=\sum_i (x_i-\mu)^2\ p(x_i)$

expected daily profit: $\mbox{E(profit)}=\sum_i (-10+4\times x_i)\ p(x_i)$

Var of profit: $\mbox{E([profit-E(profit)]^2))}=\sum_i [(-10+4\times x_i)-\mbox{E(profit)}}]^2\ p(x_i)$

RonL
• January 13th 2006, 02:22 PM
fobster
Thanks for the help, I got these answers

mean of the daily sales=11.9

variance of the daily sales=0.89

expected daily profit=37.6

and the variance of the dialy profit was 14.24