ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 387 - 390 of 404

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Question number: 387

» Probability » Central Limit Theorems for Independent Variables

MCQ▾

Question

Suppose that you have a sample of 100 values from a population with mean μ=500 and standard deviation σ=80 . What is the probability that the sample mean will be in the interval (490,510) ?

Choices

Choice (4) Response
a.

0.1056

b.

0.8944

c.

0.7888

d.

0.2112

Question number: 388

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

Which of the following are correct examples of applications of Chebyshev’s inequality?

Choices

Choice (4) Response
a.

If X be a Poisson r. v. with parameter λ . The probability that X deviates from λ by more than 2λ is atmost 14 .

b.

If X be the number of Heads in n tosses of fair coin then the probability that X deviates from μ=n2 by more than n is at most 14 and the probability that it deviates by more than 5 n is atmost 1100 .

c. Both a. and b. are correct
d. None of the above

Question number: 389

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let X,Y,Z be random variables, a,bR and g:RR . Assuming that expectations exist, we have E[X Y] = ________

Choices

Choice (4) Response
a.

E[E[X Y,Z] Y]

b.

E[X Y,g(Y)]

c.

E[X] if X and Y are independent.

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

Question number: 390

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

A hen lays N eggs, where N~Poission(λ) . Each egg hatches with probability p , independently of the other eggs. Find the probability distribution of number of chicks, Z.

Choices

Choice (4) Response
a.

Z~Poission(λp)

b.

Z~Poission(λ)

c.

Z~NegativeBinomial(n,p)

d. Question does not provide sufficient data or is vague

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