Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 177  179 of 205
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Question number: 177
» Probability » Characteristic Function
Question
For any random variable , its characteristic function is uniformly continuous on and satisfies following properties________ always.
Choices
Choice (4)  Response  

a.  , where for a complex number, denote the conjugate. 

b. 


c. 


d.  None of the above 

Question number: 178
» 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.  All of the above 

Question number: 179
» 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.  0.2643 

b.  0.7357 

c. 


d.  0.1056 
