ProbabilityDistribution Functions and Properties (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 1  6 of 11
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Question number: 1
» Probability » Distribution Functions and Properties
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
Question
A process is Martingale if and only if:
Choices
Choice (4)  Response  

a.  For all n, E [ X_{n} ] < ∞ 

b.  (X_{n}) is adapted to (F_{n}) where F_{n} is a filtration 

c.  For all n, E (X_{n + 1} X_{0}, X_{1}, …, X_{n}) =X_{n} 

d.  All a. , b. and c. are correct 

Question number: 3
» Probability » Distribution Functions and Properties
Question
In a widesense stationary process the mean function is:
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 4
» Probability » Distribution Functions and Properties
Question
In a widesense stationary process the autocorrelation R_{X} (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
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
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 
