Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 163 - 167 of 205

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Question number: 163

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let random variables Xk=N(mk,σk2) , k=1,,n be independent normal random variables. So if X=i=inXn then, which of the following is the characteristic function of X if m=i=inmi and σ2=i=inσi2 ?

Choices

Choice (4) Response
a.

eitm+σ2t2

b.

eitmσk2t22

c.

eitmσ2t22

d. All of the above

Question number: 164

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

While tossing 100 coin let H count the number of heads. Then what is the bound probability of 40<H<60 using Tchebycheff’s Inequality?

Choices

Choice (4) Response
a.

0.33

b.

0.50

c.

0.67

d.

0.25

Question number: 165

» Probability » Borel 0-1 Law

MCQ▾

Question

For each independent sequence (An)n of events AnF , we have________

Choices

Choice (4) Response
a.

P(Anforinfinitelymanyn)=0

b.

P(Anforinfinitelymanyn)=1

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

Question number: 166

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

Which of the following statement is correct?

Choices

Choice (4) Response
a.

Chebyshev’s Inequality is an special case of Kroneckers lemma.

b.

Chebyshev’s Inequality is an special case of Kolmogorov’s Inequality.

c. Question does not provide sufficient data or is vague
d. None of the above

Question number: 167

» Probability » Laws of Large Numbers

MCQ▾

Question

Suppose someone wants to estimate Prime minister’s approval rating by asking n persons drawn at random from the voter population. Let

Xi={

Now if he/she want to be 95% confident that he/she is within 0.01 of the actual approval rating then from how many (minimum number of) people he should ask?

Choices

Choice (4) Response
a.

1000

b.

10, 000

c.

25, 000

d.

50, 000

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