Probability (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 198  200 of 205
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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 

Question number: 199
» Probability » Laws of Large Numbers
Question
Let be a sequence of independent, identically distributed random variables, each having finite mean . Then for any , which of the following option is/are correct according to statement of Weak law of large number?
Choices
Choice (4)  Response  

a. 


b. 


c.  Question does not provide sufficient data or is vague 

d.  All of the above 

Question number: 200
» Probability » Kolmogorov's Inequalities
Question
For an infinite sequence, for every where be independent random variables on a common probability space with expected value and variance for . and which of the following inequality holds?
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

