ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 379 - 382 of 404

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Question number: 379

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

For a random variable X with expectation E(X)=μ , and standard deviation σ=Var(X) , which of the following inequality is correct?

Choices

Choice (4) Response

a.

P( Xμ βσ)σ2μ2

b.

P( Xμ βσ)1μ2

c.

P( Xμ βσ)σ242

d.

P( Xμ βσ)1β2

Question number: 380

» Probability » Laws of Large Numbers

MCQ▾

Question

Consider n rolls of a die. Let Xj be the outcome of the j th roll. Then, if Sn=X1++Xn is the sum of first n rolls, which of the following is correct?

Choices

Choice (4) Response

a.

P( Snn52 ϵ)0

b.

P( Snn72 ϵ)0

c.

P( Snn52 <ϵ)1

d.

P( Snn12 <ϵ)1

Question number: 381

» 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: 382

» 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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