SOLUTION: A bag contains 22 cubes, of which 11 are red. Three cubes are drawn without replacement. Let X be the number of red cubes drawn. Find the variance of X.

Algebra ->  Probability-and-statistics -> SOLUTION: A bag contains 22 cubes, of which 11 are red. Three cubes are drawn without replacement. Let X be the number of red cubes drawn. Find the variance of X.      Log On


   

Question 415070: A bag contains 22 cubes, of which 11 are red. Three cubes are drawn without replacement. Let X be the number of red cubes drawn. Find the variance of X.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The pmf is p%28x%29+=+3Cx%2A%281%2F2%29%5E%283-x%29%2A%281%2F2%29%5Ex+=+3Cx%2F8. Hence
X ----> 0 1 2 3
p(x)--> 0.125 0.375 0.375 0.125
==> mu+=+0.375+%2B+2%2A0.375+%2B+3%2A0.125+=+1.5
==> Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+3+-+1.5%5E2+=+0.75.
A shorter solution is as follows: The mean mu for a binomial experiment is n*p = 3*0.5 = 1.5, while the variance is n*p*q = 3*0.5*0.5 = 0.75. (Here, n = 3, and p = q = 0.5.)