# Thread: How to do probability >-<

1. ## How to do probability >-<

Jerseys will sell for $30. Random variable X is number of jerseys that will be sold. E(X)=100 and R is the total revenue (R=30X). What is the expected revenue. I have no idea what formula to use. I thought conditional probability because revenue is dependent on the sale of the jerseys, but the formula does not match my data, or I am writing it back the front. Why is it not$3000...?

I think if I knew the formula I could work it out~ maybe :-)

2. Originally Posted by char111
Jerseys will sell for $30. Random variable X is number of jerseys that will be sold. E(X)=100 and R is the total revenue (R=30X). What is the expected revenue. I have no idea what formula to use. I thought conditional probability because revenue is dependent on the sale of the jerseys, but the formula does not match my data, or I am writing it back the front. Why is it not$3000...?

I think if I knew the formula I could work it out~ maybe :-)
Definition of the expectation of a function of a RV:

$E(f(X))=\int f(x) p_X(x)\; dx$

so:

$
E(30X)=\int 30\; x\; p_X(x)\;dx=30 E(X)
$

where the integrals are over the support of $p_X$.

Make the obvious modification or interpretation for a discrete RV.

CB

3. Thanks Captain Black~ obviously I have no idea because I have not seen this formula before in class nor can I find it in my book.

100 x (30x100)...is that how I plug in my numbers...?

This topic just confuses me the more I try to understand it~ give me SPSS anytime :-)