Question

It is known that there is a defective chip on a computer board that contains 8 chips. A technician tests the chips one at a time until the defective chip is found. Assume that the chip to be tested is selected at random without replacement. Let the random variable X

denote the number of chips tested. What is the mean of X?

Answer 1

Here there is a defective chip on a computer board that contains 8 chips.  A technician tests the chips one at a time until the defective chip is found. Assume that the chip to be tested is selected at random without replacement.

Let the random variable X denote the number of chips tested.

so here as we can that X can take values from 1 to 8.

p(x = 1) = P(First selected chip is a defective chip) = 1/8

p(x = 2) = P(Good chip selected as first chip) * P(Second chip selected is bad chip) = 7/8 * 1/7 = 1/8

similalry,

P(x) = 1/8 ; x = 1,2,3,4,5,6,7,8

Mean of X = E[x] = 1/8 * (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 4.5