A box contains 7 items, 4 of which are defective. a random sample of 3 items are taken from the box. Let X be the number of defective items in the sample. 1.Find the probability mass function of X. 2.Find the mean and the variance of X.
here X follows hypergeometric distribution with parameter n=3 ; k=4 and N =7
probability mass function of X =P(X=x)=P(getting x defective from 4 and 3-x good items from 3)
from above formula
|E(x) =μ=||ΣxP(x) =||1.7143|
|E(x2) =||Σx2P(x) =||3.4286|
from above mean =1.7143 (this can directly be derived from formula nk/N =3*4/7=1.7143)
and variance =0.490 ( this can directly be derived from formula nk/N(1-k/N)*(N-n)/(N-1))
Get Answers For Free
Most questions answered within 1 hours.