Probability (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 189  192 of 205
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Question number: 189
» Probability » Tchebycheff's Inequalities
Question
Which of the following are correct examples of applications of Chebyshev’s inequality?
Choices
Choice (4)  Response  

a.  If be a Poisson r. v. with parameter . The probability that deviates from by more than is atmost . 

b.  If be the number of Heads in tosses of fair coin then the probability that deviates from by more than is at most and the probability that it deviates by more than 5 is atmost . 

c.  Both a. and b. are correct 

d.  None of the above 

Question number: 190
» Probability » Mathematical Expectation and Conditional Expectation
Question
Let be random variables, and . Assuming that expectations exist, we have = ________
Choices
Choice (4)  Response  

a. 


b. 


c.  if and are independent. 

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

Question number: 191
» Probability » Moment and Probability Generating Functions
Question
A hen lays eggs, where . Each egg hatches with probability , independently of the other eggs. Find the probability distribution of number of chicks,
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  Question does not provide sufficient data or is vague 

Question number: 192
» Probability » Central Limit Theorems for Independent Variables
Question
Let be a ramdom variable and . A sample of size is taken from this population. What is the probability that the sum of these observations is less than ?
Choices
Choice (4)  Response  

a. 


b.  0.0062 

c. 


d. 

