ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 379 - 382 of 471

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Question number: 379

» 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 be a Poisson r. v. with parameter . The probability that deviates from by more than is atmost .

b.

If be the number of Heads in tosses of fair coin then the probability that deviates from by more than is at most and the probability that it deviates by more than 5 is atmost .

c.

Both a. and b. are correct

d.

None of the above

Question number: 380

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let be random variables, and . Assuming that expectations exist, we have = ________

Choices

Choice (4) Response

a.

b.

c.

if and are independent.

d.

All a. , b. and c. are correct

Question number: 381

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

A hen lays eggs, where . Each egg hatches with probability , independently of the other eggs. Find the probability distribution of number of chicks,

Choices

Choice (4) Response

a.

b.

c.

d.

Question does not provide sufficient data or is vague

Question number: 382

» Probability » Central Limit Theorems for Independent Variables

MCQ▾

Question

Let be a ramdom variable and . A sample of size is taken from this population. What is the probability that the sum of these observations is less than ?

Choices

Choice (4) Response

a.

b.

0.0062

c.

d.

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