Probability-Modes of Convergences of Sequences of Random Variables (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 8 - 10 of 11

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Question number: 8

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

MCQ▾

Question

Let for and let Let and be the corresponding probability density functions and let and be the corresponding distribution functions. Then which of the following option is/are correct?

Choices

Choice (4) Response

a.

as for all

b.

as

c.

as for all

d.

None of the above

Question number: 9

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

MCQ▾

Question

Suppose that is a sequence of independent random variables with , ; , then the following option is correct?

Choices

Choice (4) Response

a.

almost everywhere

b.

as

c.

in probability

d.

Question does not provide sufficient data or is vague

Question number: 10

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

MCQ▾

Question

Consider the following statements and then choose the option in which the given statements are equivalent.

I)

II)

III) for every

IV) for every

V) for every

Choices

Choice (4) Response

a.

II and IV

b.

I, III, V

c.

I, V

d.

Question does not provide sufficient data or is vague

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