Question

A batch of 7 lamps contains two defective ones. A restaurant acquires three of these lamps. Let x be the number of defective lamps. Find the distribution of x. expected value and standard deviation

Answer 1

Total lamps ( N ) = 7 , Defective lamps ( M ) = 2 , Non defective lamps ( N-M ) = 5

Sample size (n) = 3

x be the number of defective lamps , x follows hypoergeometric distribution .

P( X = x) = x =0,1,2..n

Therefore ,

Expected value = =

Expected value  = 0.857143

Variance = = =

Variance = 0.408163

Standard deviation = =

Standard deviation = 0.638877