There are 2 defective items in a group of 10 A sample of 8 i

There are 2 defective items in a group of 10. A sample of 8 items is taken randomly from the group. Let the random variable X be the number of defective items in the sample. Construct the probability mass function (pmf) of X. Compute E(X). Compute Var (X)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

b)
Mean ( np ) = 8 * (2/10) 1.6
c)
Standard Deviation ( npq )= 8*0.2*0.8 = 1.1314
Variance ( npq )= 8*0.2*0.8 = 1.28