Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 195  198 of 205
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Question number: 195
» Probability » Moment and Probability Generating Functions
Question
Suppose that is a random variable taking values in N. The probability generating function of will satisfy the following properties.
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  All of the above 

Question number: 196
» Probability » Kolmogorov's Inequalities
Question
Which of the following statement is correct?
Choices
Choice (4)  Response  

a.  Kolmogorov’s Inequality is a special case of Martingale Maximal Inequality. 

b.  Kolmogorov’s Inequality is a special case of Chebyshev’s Inequality. 

c.  All of the above 

d.  None of the above 

Question number: 197
» Probability » Uniqueness and Continuity Theorems
Question
Let be random variables on such that,
Then, which of the following is correct?
Choices
Choice (4)  Response  

a.  converges for all . 

b.  does not converges for all . 

c.  is always increasing. 

d.  None of the above 

Question number: 198
» Probability » Kolmogorov's 01 Law
Question
Consider an infinite random stream of fair coin tosses: an infinite sequence of 0′s and 1′s, chosen IID with equal probabilities at each step. Call the result of the coin toss (these variables generate the sample space). Which of the following is correct regarding the following limit?
Choices
Choice (4)  Response  

a.  Strong law of large numbers states that the limit exists, with probability 0. 

b.  According to Kolmogorov’s 0  1 law the limit never exist. 

c.  According to Kolmogorov’s 0  1 law if there is no limit then it’s probability is 1. 

d.  Question does not provide sufficient data or is vague 
