Probability-Modes of Convergences of Sequences of Random Variables (ISS 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 Equation for Equation and let Equation Let Equation and Equation be the corresponding probability density functions and let Equation and Equation be the corresponding distribution functions. Then which of the following option is/are correct?

Choices

Choice (4) Response

a.

Equation as Equation for all Equation

b.

Equation as Equation

c.

Equation as Equation for all Equation

d.

None of the above

Question number: 9

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

MCQ▾

Question

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

Choices

Choice (4) Response

a.

Equation almost everywhere

b.

Equation as Equation

c.

Equation 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) Equation

II) Equation

III) Equation for every Equation

IV) Equation for every Equation

V) Equation for every Equation

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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