ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 367  371 of 472
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Question number: 367
» Probability » Laws of Large Numbers
Question
Let be a sequence of independent, identically distributed random variables, each having finite mean . Then, which of the following option is/are correct according to statement of Strong law of large number?
Choices
Choice (4)  Response  

a.  
b. 
 
c.  None of the above  
d.  Question does not provide sufficient data or is vague 
Question number: 368
» Probability » Central Limit Theorems for Independent Variables
Question
The amount of regular unleaded gasoline purchased every week at a gas station near Palampur follows the normal distribution with mean gallons and standard deviation gallons. The starting supply of gasoline is gallons, and there is a scheduled weekly delivery of gallons. Find the probability that, after weeks, the supply of gasoline will be below gallons.
Choices
Choice (4)  Response  

a.  0.1056  
b.  0.2643  
c.  0.7357  
d. 

Question number: 369
» Probability » Tchebycheff's Inequalities
Question
For a random variable with expectation , and standard deviation , which of the following inequality is correct?
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 370
» Probability » Laws of Large Numbers
Question
Consider rolls of a die. Let be the outcome of the ^{th} roll. Then, if is the sum of first n rolls, which of the following is correct?
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 371
Question
Suppose are independent events with where . If then, which of the following is correct?
Choices
Choice (4)  Response  

a.  a. s  
b.  a. s  
c.  does not converge.  
d.  in probability. 