WeeG

04-27-2010, 10:01 AM

Hi,

got a little question regarding Hypergeometric distribution.

We mix in an urn 15 coins. 5 coins of 1 pound, 5 coins of 50 pens and 5 coins of 20 pens.

we choose randomly and without replacement 4 coins. X is defined as the number of coins of 1 pound.

a. what is the probability function of X, calculate E(X) and Var(X)

b. what is the probability to have maximum 2 coins of 20 pens ?

c. what is the probability to have at least 1 coin of 50 pens ?

On 'a' I did:

P(X=k)=((5 over k)*(10over 4-k)) / (15 over 4)

E(X)=4*5=20

Var(X)=[4*5*(15-4)*(15-5)] / [225*(15-1)]

is it correct ? how to solve b and c ? a hint would be appreciated !

got a little question regarding Hypergeometric distribution.

We mix in an urn 15 coins. 5 coins of 1 pound, 5 coins of 50 pens and 5 coins of 20 pens.

we choose randomly and without replacement 4 coins. X is defined as the number of coins of 1 pound.

a. what is the probability function of X, calculate E(X) and Var(X)

b. what is the probability to have maximum 2 coins of 20 pens ?

c. what is the probability to have at least 1 coin of 50 pens ?

On 'a' I did:

P(X=k)=((5 over k)*(10over 4-k)) / (15 over 4)

E(X)=4*5=20

Var(X)=[4*5*(15-4)*(15-5)] / [225*(15-1)]

is it correct ? how to solve b and c ? a hint would be appreciated !