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

MCQ▾

Question

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

Choices

Choice (4) Response

a.

Equation for each Equation but Equation

b.

The distribution of Equation converges to the distribution of Equation as Equation

c.

Equation as Equation for all Equation

d.

All a. , b. and c. are correct

Question number: 2

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

MCQ▾

Question

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

Choices

Choice (4) Response

a.

Equation as Equation Equation -th mean

b.

Equation almost everywhere

c.

Equation as Equation in probability

d.

All of the above

Question number: 3

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

MCQ▾

Question

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

Choices

Choice (4) Response

a.

Exponential distribution with parameter 1

b.

Poisson distribution with parameter 1

c.

Laplace distribution with location parameter 0 and scale parameter 1

d.

None of the above

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