Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 199 - 200 of 205

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Question number: 199

» Probability » Laws of Large Numbers

MCQ▾

Question

Let X1,X2, be a sequence of independent, identically distributed random variables, each having finite mean μ=E(Xk),k=1, 2,.. . Then for any ε>0 , which of the following option is/are correct according to statement of Weak law of large number?

Choices

Choice (4) Response
a.

limnP{ X1++Xnnμ ε}=0

b.

P{limnX1++Xnn=μ}=1

c. Question does not provide sufficient data or is vague
d. All of the above

Question number: 200

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

For an infinite sequence (Xk)k , for every c>0, where , X1,X2,:ΩR be independent random variables on a common probability space (Ω,F,P), with expected value E[Xk]=0 and variance Var[Xk]<+ for k=1, 2 . and Sk=X1+X2+ which of the following inequality holds?

Choices

Choice (4) Response
a.

P(Supk Sk c)1ck=1VarXk

b.

P(Infk Sk c)1c2k=1VarXk

c.

P(Supk Sk c)1c2k=1VarXk

d.

P(Supk Sk c)1c2k=1VarXk2

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