Probability-Modes of Convergences of Sequences of Random Variables (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 3 of 11

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Question number: 1

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

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MCQ▾

Question

Suppose that has the discrete uniform distribution on for each and let denote the probability density function of Let have the continuous uniform distribution on the interval . Then which of the following is correct option?

Choices

Choice (4) Response

a.

as for all

b.

for each but

c.

The distribution of converges to the distribution of as

d.

All a. , b. and c. are correct

Question number: 2

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

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MCQ▾

Question

Suppose that is a sequence of random variables (defined on the same probability space) and that the distribution of converges to the distribution of the constant . Then________.

Choices

Choice (4) Response

a.

as -th mean

b.

as in probability

c.

almost everywhere

d.

None of the above

Question number: 3

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

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MCQ▾

Question

Consider a random permutation of the elements in the set . We say that s match occurs at position . If denotes the number of matches, then the distribution of converges to ________ as .

Choices

Choice (4) Response

a.

Exponential distribution with parameter 1

b.

Laplace distribution with location parameter 0 and scale parameter 1

c.

Poisson distribution with parameter 1

d.

None of the above

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