Kindly solve t following questions?

\f2. (10 points) (The Weak Law of Large Numbers) In order to estimate f, the true fraction of smokers in a large population, Alvin selects n people at random. His estimator Mn is obtained by dividing Sn, the number of smokers in his sample, by N, i.e., Mn = Sn. Alvin chooses the sample size n to be the smallest possible number for which the Chebyshev inequality yields a guarantee that P(IMn - f1 2 6) 58, where e and o are some prespecified tolerances. Determine how the value of n recommended by the Chebyshev inequality changes in the following cases. (a) (5 points) The value of e is reduced to half its original value. (b) (5 points) The value of o is reduced to half its original value.Markov inequality For a random variable X 2 0 with mean / > 0, and any numbert > 0: P(X >D)SH. Note that the Markov inequality is restricted to non-negative random variables. Chebyshev inequality For a random variable X with (finite) mean / and variance of, and for any number t 2: 0, P(X -#| 20)ST. Remark: When Markov inequality is applied to (X" - /)", we obtain Chebyshev's inequality. Markov inequality is also used in the proof of Hoeffding's inequality. Hoeffding versus Chebyshev 4 points possible (graded) Let X], X2, ...;X, " Unif (0, b) be n i.i.d. uniform random variables on the interval [0, b] for some positive b. Suppose n is small (i.e. in