Probability-Tchebycheff's Inequalities (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 5 of 6

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Question number: 1

» 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: 2

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

Let X~Binomial(n,p) . Using Chebyshev’s inequality, find an upper bound on P(Xnα) , where p<α<1 . Evaluate the bound for p=12 and =34 .

Choices

Choice (4) Response
a.

1n

b.

2n2

c.

4n

d. All of the above

Question number: 3

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

If X follows an exponential distribution with λ=1 , then what is the bound of P(X3) using Tchebycheff’s Inequality?

Choices

Choice (4) Response
a.

16

b.

14

c.

15

d.

12

Question number: 4

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

For a random variable X with expectation E(X)=μ , and standard deviation σ=Var(X) , which of the following inequality is correct?

Choices

Choice (4) Response
a.

P( Xμ βσ)σ2μ2

b.

P( Xμ βσ)1μ2

c.

P( Xμ βσ)σ242

d.

P( Xμ βσ)1β2

Question number: 5

» 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

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