Probability-Laws of Large Numbers (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 3 of 5

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Question number: 1

» Probability » Laws of Large Numbers

MCQ▾

Question

Suppose someone wants to estimate Prime minister’s approval rating by asking n persons drawn at random from the voter population. Let

Xi={

Now if he/she want to be 95% confident that he/she is within 0.01 of the actual approval rating then from how many (minimum number of) people he should ask?

Choices

Choice (4) Response

a.

1000

b.

10, 000

c.

25, 000

d.

50, 000

Question number: 2

» 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, which of the following option is/are correct according to statement of Strong law of large number?

Choices

Choice (4) Response

a.

P{limnX1++Xnn=μ}=1

b.

limnP{ X1++Xnnμ ε}=0

c.

None of the above

d.

All of the above

Question number: 3

» 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

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