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}:

P=(1/21/41/41/31/31/3100)

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.

mX(t)=ct

b.

mX(t)=ct

c.

mX(t)=ct2

d.

mX(t)=c

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.

t

b.

Autocorrelation does not depend on s or t

c.

s

d.

st

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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