Probability-Laws of Large Numbers (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 4 - 5 of 5

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Question number: 4

» Probability » Laws of Large Numbers

MCQ▾

Question

Suppose we choose at random n numbers from the interval [0, 1] with uniform distribution. If Xi describes the i th choice and Sn=X1++Xn , then which of the following is correct?

Choices

Choice (4) Response

a.

limnP( Snn12 <ϵ)=0

b.

limnP( Snn12 ϵ)=0

c.

limnP( Snn72 ϵ)=0

d.

limnP( Snn32 ϵ)=0

Question number: 5

» 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

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