1. ## 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?

2. 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

3. 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