Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 201 - 204 of 205

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Question number: 201

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

Suppose that we roll a standard fair die 100 times. Let X be the sum of the numbers that appear over the 100 rolls. Find the bound using Chebyshev’s inequality for P( X350 50) .

Choices

Choice (4) Response
a.

3225

b.

940

c.

760

d.

1350

Question number: 202

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

If X~Binomial(m,p) and Y~Binomial(n,p) are independent, then what is the distribution of +Y ?

Choices

Choice (4) Response
a.

X+Y~Binomial(mn,p)

b.

X+Y~Binomial(mn,p)

c.

X+Y~Binomial(mn,p)

d. None of the above

Question number: 203

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him safety after 3 hours of travel, the second door leads to a tunnel that will return him to the mine after 5 hours of travel. The third door leads to a tunnel that will return him to the mine after 7 hours of travel. If we assume that the miner is at all times equally likely to choose any one of the doors, find the expected time for him to get to safety.

Choices

Choice (4) Response
a.

3

b.

5

c.

15

d. Question does not provide sufficient data or is vague

Question number: 204

» Probability » Kolmogorov's 0-1 Law

MCQ▾

Question

Which of the following is correct regarding Kolmogorov’s zero-one law?

Choices

Choice (4) Response
a.

It is even valid for sequence of dependent random variables.

b.

A tail σ -algebra contains only events of probability 0 or 1.

c. Question does not provide sufficient data or is vague
d. All of the above

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