statistical math problem

illusive01

Well, im stuck on a silly problem i cant understand.

a man got to take 20 pies, (15 of em are made with green apples, other five are made out of red apples) he has to identify how many pie are made out of green apple, but he has no idea, so he picks randomly.

i need to find the variance of Y= the number of green apple pie correctly identified.

i can pretty much link the problem to discret statistical laws (either a binomial or a hypergeometric) but for the life out of me, i cant understand how to begin the problem.

any suggestion or help?

Smug Duckling

So Y is basically:

Y = 0 if he chose incorrectly
Y = 1 if he chose correctly

?

If so, the variance would be (since var = sum(x^2 * P(x)) - (sum(x * P(x))^2):

Var
= 0 * P(incorrect) + 1 * P(correct) - (0 * P(incorrect) + 1 * P(correct))^2
= P(correct) - P(correct)^2
= ...

Then you need to know the way in which he chose randomly. I assume it's some kind of uniform distribution that he's picking from, but what's the maximum he could choose?

EDIT: Fixed definition of variance.

illusive01

from what i can understand, he can decide there is 1 to 15 green apple pie, so he random pick (p= .5?) which one they are

Folken Fanel

illusive01 wrote: »

from what i can understand, he can decide there is 1 to 15 green apple pie, so he random pick (p= .5?) which one they are

You said there are 20 pies. So probability of picking a green apple pie randomly is 15/20

Smug Duckling

So to clarify, are you trying to figure out the variance of his guess? So he guesses for example 1, 6, 17, 3, 3, 20, 3, 8, and you want to figure out the theoretical variance of this?

illusive01

yes,

there is 2 versions of the problem, the first one where he dosent know how many green apple pie there is. (the one im struggling with)

and the second where he knows there is 15 green apple pie out of the 20, i figured out this one, as it follow the hypergeometric rules :

n * p * q * (N-n)/(N-1)

15 * (15/20) * (1 - 15/20)) * (20-15)/(20-1)

but for the first one, i cant figure out exacly what are the odds for each of his choice that he picks a green apple pie.