Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1  6 of 205
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Question number: 1
» Probability » Probability Distributions » Poisson
Question
The telegraph function has autocorrelation function of:
Choices
Choice (4)  Response  

a. 


b.  1 

c. 


d. 


Question number: 2
» 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: 3
» 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: 4
» 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: 5
» 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: 6
» 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. 
