Probability-Modes of Convergences of Sequences of Random Variables (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 4 - 7 of 11

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Question number: 4

» Probability » Modes of Convergences of Sequences of Random Variables » With Probability One

MCQ▾

Question

If XnX as n with probability 1 then,

Choices

Choice (4) Response
a.

XnX as n in probability.

b.

XnX as n in r-th mean.

c.

XnX as n almost everywhere.

d. Question does not provide sufficient data or is vague

Question number: 5

» Probability » Modes of Convergences of Sequences of Random Variables » In Mean Square

MCQ▾

Question

If XnXasn in mean, then ________.

Choices

Choice (4) Response
a.

XnX almost everywhere

b.

XnXasn in distribution.

c.

XnXasn in probability.

d. Both b. and c. are correct

Question number: 6

» Probability » Modes of Convergences of Sequences of Random Variables » In Mean Square

MCQ▾

Question

If j<k<l, then XnXasn in the k -th mean implies ________.

Choices

Choice (4) Response
a.

XnXasn in l -th mean.

b.

XnXasn in j -th mean.

c.

XnX almost everywhere.

d. All of the above

Question number: 7

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Consider the following events and then choose the option in which the given events are same.

I) Xn does not converges to X as n .

II) Xn converges to X as n

III) For some ϵ>0, XnX >ϵ for infinitely many nN+

IV) For some ϵQ+, XnX <ϵ for infinitely many nN+ .

Choices

Choice (4) Response
a.

I and III

b.

II and III

c.

II and IV

d. None of the above

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