# Probability-Distribution Functions and Properties (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 6 of 11

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## Question number: 1

» Probability » Distribution Functions and Properties

MCQ▾

### Question

Consider the following Markov chain with state space {a, b, c}:

What is the probability that the chain in state b when it is already in state b.

### Choices

Choice (4) Response

a.

0.5

b.

0.0

c.

0.33

d.

0.2

## Question number: 2

» Probability » Distribution Functions and Properties

MCQ▾

### Question

A process is Martingale if and only if:

### Choices

Choice (4) Response

a.

For all n, E [| Xn| ] < ∞

b.

(Xn) is adapted to (Fn) where Fn is a filtration

c.

For all n, E (Xn + 1| X0, X1, …, Xn) =Xn

d.

All a. , b. and c. are correct

## Question number: 3

» Probability » Distribution Functions and Properties

MCQ▾

### Question

In a wide-sense stationary process the mean function is:

### Choices

Choice (4) Response

a.

b.

c.

d.

## Question number: 4

» Probability » Distribution Functions and Properties

MCQ▾

### Question

In a wide-sense stationary process the autocorrelation RX (t, s) is a function is:

### Choices

Choice (4) Response

a.

b.

Autocorrelation does not depend on s or t

c.

d.

## Question number: 5

» Probability » Distribution Functions and Properties

MCQ▾

### Question

In an Irreducible Markov chain:

### Choices

Choice (4) Response

a.

You can move from one state to another only in 1 direction

b.

You can only move between 1 of two states

c.

All the states can communicate with each other

d.

There is at least one state when you can go with 0 probability.

## Question number: 6

» Probability » Distribution Functions and Properties

MCQ▾

### Question

Which of the following is a property of a renewable process?

### Choices

Choice (4) Response

a.

Inter arrival intervals are negative

b.

Inter arrival intervals may be identically distributed

c.

Inter arrival intervals are positive

d.

None of the above

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