# Probability mass function - correct solution?

• October 7th 2012, 08:01 AM
FireTheft
Expected Value - correct solution?
Consider the following game. Everybody has to press a button on a machine which results
in one of three possible outcomes:

The result 1 has probability p1 = 1/4.
The result 2 has probability p2 = 1/3.
The result 3 has probability p3 = 5/12.

Now everybody presses the button three times and adds up the results. This is the result
of the game.

1. Calculate the expected value for the game described above.

is 6.5 correct? (Nod)

• October 7th 2012, 09:10 AM
Plato
Re: Expected Value - correct solution?
Quote:

Originally Posted by FireTheft
Consider the following game. Everybody has to press a button on a machine which results in one of three possible outcomes:
The result 1 has probability p1 = 1/4.
The result 2 has probability p2 = 1/3.
The result 3 has probability p3 = 5/12.
Now everybody presses the button three times and adds up the results. This is the result of the game.

Please explain exactly how this game is played.
Is there just one button? If so, are the results purely random?
Can a contestant get say (3,3,3) or (1,2,1)?
• October 7th 2012, 09:27 AM
FireTheft
Re: Expected Value - correct solution?
There is just one button and in my opinion the results are purely random....

Yes I would say a contestant get is able to say (3,3,3) or (1,2,1)...

The text above is all Info I got from my Math teacher....

THX
• October 7th 2012, 09:51 AM
Plato
Re: Expected Value - correct solution?
Quote:

Originally Posted by FireTheft
There is just one button and in my opinion the results are purely random....
Yes I would say a contestant get is able to say (3,3,3) or (1,2,1)...

We will assume that is the case, although it is not clear.
The outcomes are $3,~4,~5,~6,~7,~8,\text or }~9$
The outcomes $3~\&~9$ can happen in one way each.

Using this generating polynomial you can read of the coefficients.
The term $7x^6$ tells us $(X = 6)$ happen seven ways.
• October 8th 2012, 09:56 AM
FireTheft
Re: Probability mass function - correct solution?
I already did it like this and my solution would be 6.5...
can someone affirm this?

And then the following was asked:

Calculate the the variance and the third moment around the expected value for the
game described above.

So for the variance I used this formula....

Discrete random variable
If the random variable X is discrete with probability mass function x1 7!
p1; : : : ; xn 7! pn, then
Var(X) = Sum of pi times (xi - ev)^2
where pi=probability for i
xi = value for i
ev= expected value

So started with 1/64*(3-6,5)^2 + 1/16*(4-6,5)^2 and so on...
my result is 23/12....

I hope this is correct....

But how do I calculate the skewness now?

Attachment 25109

for μ I would again take the expected value, but what do I insert fpr X and E???