ProbabilityModes of Convergences of Sequences of Random Variables (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1  3 of 11
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Question number: 1
» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution
Question
Suppose that has the discrete uniform distribution on for each and let denote the probability density function of Let have the continuous uniform distribution on the interval . Then which of the following is correct option?
Choices
Choice (4)  Response  

a.  for each but 

b.  The distribution of converges to the distribution of as 

c.  as for all 

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

Question number: 2
» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution
Question
Suppose that is a sequence of random variables (defined on the same probability space) and that the distribution of converges to the distribution of the constant . Then________.
Choices
Choice (4)  Response  

a.  as th mean 

b.  almost everywhere 

c.  as in probability 

d.  All of the above 

Question number: 3
» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution
Question
Consider a random permutation of the elements in the set . We say that s match occurs at position . If denotes the number of matches, then the distribution of converges to ________ as .
Choices
Choice (4)  Response  

a.  Exponential distribution with parameter 1 

b.  Poisson distribution with parameter 1 

c.  Laplace distribution with location parameter 0 and scale parameter 1 

d.  None of the above 
