Question

Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.

Answer 1

Let X denote the Random Variable defined by the number of defective items.

P(X = 0) = `4/6 xx 3/5 = 2/5`

P(X = 1) = `2 xx (2/6 xx 4/5) = 8/15`

P(X = 2) = `2/6 xx 1/5 = 1/15`

xi	0	1	2
pi	`2/5`	`8/15`	`1/15`
pixi	0	`8/15`	`2/15`

Mean = `sump_ix_i = 10/15 = 2/3`