# Expected value

1. Mar 30, 2013

### ParisSpart

On a random day a store monetize P. The density of random variable P is given by the following table:
n -20 0 10 20 30
f (n) .1 .1 .4 .3 .1

From this profit the store pays a tax T that is given by

T = 0 if P<15
and T=0.16*P if P>=15

What is the expected value of tax E{T} that pays the store each day

i am doing it like this:
E(T)=0+0+0+0.16*20*3+0.16*30*1=14.4 but the quiz says tha its not correct.what ai am doing wrong?

2. Mar 30, 2013

### Staff: Mentor

A simple cross-check: What is the maximal amount of tax paid? Do you see any problem if you compare that to your calculated expectation value?

Hint: It is a problem with decimal points.

3. Mar 30, 2013

### ParisSpart

what do u mean with decimal points?

4. Mar 30, 2013

### Staff: Mentor

Did you do the cross-check I suggested?

[highlight].[/highlight]1 <- this is a decimal point

5. Mar 30, 2013

### ParisSpart

i dont understand how to do it.....

6. Mar 30, 2013

### Staff: Mentor

I don't understand where the problem is. Which P corresponds to the maximal tax? How much tax is paid there?

Can the expectation value be above the maximal possible value?

7. Mar 30, 2013

### ParisSpart

p whick corresponds is 3when n=30?

8. Mar 30, 2013

### Ray Vickson

You are not using the definition of *expected value*? Do you know what it is? If you do know, just use it in this problem. If you do not know it you need to study some material first before attempting this problem.

9. Mar 30, 2013

### ParisSpart

i know how to use any expected value but how i can use it here because i dont understand what is .1 .4 with f(n)......

10. Mar 30, 2013

### Staff: Mentor

Those are the probabilities to get the corresponding money.
With a probability of 0.1, the store loses 20. With a probability of 0.1, it gains nothing, and so on.

11. Mar 30, 2013

### ParisSpart

its 1,44 i found it