Probability-Borel 0-1 Law (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 3 of 3

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Question number: 1

» Probability » Borel 0-1 Law

MCQ▾

Question

For each independent sequence (An)n of events AnF , we have________

Choices

Choice (4) Response

a.

P(Anforinfinitelymanyn)=0

b.

P(Anforinfinitelymanyn)=1

c.

Both a. and b. are correct

d.

None of the above

Question number: 2

» Probability » Borel 0-1 Law

MCQ▾

Question

Suppose A1,A2,,An, are independent events with npn= where pn=P(An) . If Xn=i=1n1Aii=1npi then, which of the following is correct?

Choices

Choice (4) Response

a.

Xn1 a. s

b.

Xn0 a. s

c.

Xn does not converge.

d.

Xn0 in probability.

Question number: 3

» Probability » Borel 0-1 Law

MCQ▾

Question

Let X1,X2, be independent and equidistributed. Then which of the following is correct regarding E( Xk ) ?

Choices

Choice (4) Response

a.

If E( Xk ) are infinite then Xn will be larger than n infinitely many times with probability 0.

b.

If E( Xk ) are finite then Xn will be larger than n infinitely many times with probability 1.

c.

None of the above

d.

Question does not provide sufficient data or is vague

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