Let the random variable yn have a distribution that is b(n, p).

(a) prove that yn/n converges in probability to p. this result is one form of the weak law of large numbers.

(b) prove that 1 − yn/n converges in probability to 1 − p.

(c) prove that (yn/n)(1 − yn/n) converges in probability to p(1 − p).

Step-by-step explanation:

Let the random variable have a distribution thst id b(n, p)

a)

Hence, it is obtained that

Hence, it is obtained that

C)

As it was shown that obtained the following

Difference the above

Hence the following expression has been obtained.

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step-by-step explanation:

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