# Probability-Modes of Convergences of Sequences of Random Variables (ISS 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 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.

for each but

b.

The distribution of converges to the distribution of as

c.

as for all

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 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.

almost everywhere

c.

as 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 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.

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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