Q3) Answer the following: P = п a) State the WLLN for i.i.d. case. b) Let X1, X2, .....be iid RVs with common law b(i,p)

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Q3) Answer the following: P = п a) State the WLLN for i.i.d. case. b) Let X1, X2, .....be iid RVs with common law b(i,p). Then find the value a which satisfies X → a as nowhere = Sn and Sn = {k=1Xk- c) Find Mn(t): the MGF of Sn. And find its limit M(t). d) State the central limit theorem (CLT). e) Let X1, X2, .....be iid RVs with common law b(i,p). Find E(Sn) and var(Sn) and use the CLT to Sn-E(Sn) find the limiting distribution of vvar(sn) 2