Finding the expected value of tax from a discrete profit distribution

[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?

 

[mfb]

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.

 

[ParisSpart]

what do u mean with decimal points?

 

[mfb]

Did you do the cross-check I suggested?

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

 

[ParisSpart]

i don't understand how to do it...

 

[mfb]

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?

 

[ParisSpart]

p whick corresponds is 3when n=30?

 

[Ray Vickson]

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?

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.

 

[ParisSpart]

i know how to use any expected value but how i can use it here because i don't understand what is .1 .4 with f(n)...

 

[mfb]

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.

 

[ParisSpart]

its 1,44 i found it