ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 400  403 of 458
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Question number: 400
» Probability » Tchebycheff's Inequalities
Question
Suppose that we roll a standard fair die 100 times. Let be the sum of the numbers that appear over the 100 rolls. Find the bound using Chebyshev’s inequality for .
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 401
» Probability » Moment and Probability Generating Functions
Question
If and are independent, then what is the distribution of ?
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  None of the above 

Question number: 402
» Probability » Mathematical Expectation and Conditional Expectation
Question
A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him safety after 3 hours of travel, the second door leads to a tunnel that will return him to the mine after 5 hours of travel. The third door leads to a tunnel that will return him to the mine after 7 hours of travel. If we assume that the miner is at all times equally likely to choose any one of the doors, find the expected time for him to get to safety.
Choices
Choice (4)  Response  

a.  3 

b.  5 

c.  15 

d.  Question does not provide sufficient data or is vague 

Question number: 403
» Probability » Kolmogorov's 01 Law
Question
Which of the following is correct regarding Kolmogorov’s zeroone law?
Choices
Choice (4)  Response  

a.  It is even valid for sequence of dependent random variables. 

b.  A tail algebra contains only events of probability 0 or 1. 

c.  Question does not provide sufficient data or is vague 

d.  All of the above 
