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 Equation , Equation be independent normal random variables. So if Equation then, which of the following is the characteristic function of Equation if Equation and Equation ?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

All of the above

Question number: 164

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

While tossing 100 coin let Equation count the number of heads. Then what is the bound probability of Equation 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 Equation of events Equation , we have________

Choices

Choice (4) Response

a.

Equation

b.

Equation

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 Equation persons drawn at random from the voter population. Let

Equation

Now if he/she want to be Equation confident that he/she is within Equation 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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