6.6. A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by N₁ the number of tests made until the first defective is identified and by N₂ the number of additional tests until the second defective is identi- fied. Find the joint probability mass function of N₁ and N₂.

A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 8 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured and pays a fixed sum on death. All 8 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. Part a) What is the expected number of policies that will pay out before the insured parties have reached age 61? Part b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? Part c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?

Suppose that three balls are randomly chosen without replacement from a box containing 4 white and 7 black balls. Let Xi be 1 if i th ball selected is white, ant let it be 0 otherwise.a. Write down Probability mass functions of X1, X2 and X3 in tabular form;b. Write down the joint probability mass function of X1, X2;c. Find the joint probability mass function of X1, X2 and X3. Repeat this problem, when the ball is replaced in the box before the next selection. Please justify your answers. Thanks!

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