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 Equation as Equation with probability 1 then,

Choices

Choice (4) Response

a.

Equation as Equation in probability.

b.

Equation as Equation in r-th mean.

c.

Equation as Equation 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 Equation in mean, then ________.

Choices

Choice (4) Response

a.

Equation almost everywhere

b.

Equation in distribution.

c.

Equation 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 Equation then Equation in the Equation -th mean implies ________.

Choices

Choice (4) Response

a.

Equation in Equation -th mean.

b.

Equation in Equation -th mean.

c.

Equation 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) Equation does not converges to Equation as Equation .

II) Equation converges to Equation as Equation

III) For some Equation for infinitely many Equation

IV) For some Equation for infinitely many Equation .

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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