Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 184  187 of 205
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Question number: 184
» Probability » Mathematical Expectation and Conditional Expectation
Question
If is the number of points rolled with a balanced die, find the expected value of .
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  None of the above 

Question number: 185
» Probability » Moment and Probability Generating Functions
Question
Suppose that and are independent random variables taking values in N, with probability generating functions and having radii of convergence and , respectively. Then the probability generating function of is given by________ for .
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  None of the above 

Question number: 186
» Probability » Kolmogorov's 01 Law
Question
Consider the random graph we get from the square grid by keeping each edge with probability p (0 < p < 1 some predetermined constant) IID, and deleting it otherwise (this is percolation on the square grid, and has been extensively studied). Which of the following is correct regarding an infinite connected component somewhere in the graph?
Choices
Choice (4)  Response  

a.  There always exist finite connected component. 

b.  Existence of an infinite connected component is impossible. 

c.  Probability that there exists an infinite connected component is 0.5. 

d.  None of the above 

Question number: 187
» Probability » Mathematical Expectation and Conditional Expectation
Question
Let be an exponential random variable with parameter . It’s characteristic function is________.
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  Question does not provide sufficient data or is vague 
