ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 343 - 347 of 472

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Question 343

Distributions of Functions of Random Variables

Question

MCQ▾

Suppose and are independent exponential random variables with parameter . If . Then the marginal distribution of or will follow ________.

Choices

Choice (4)Response

a.

Poisson distribution with parameter

b.

Exponential distribution with parameter

c.

Exponential distribution with parameter

d.

None of the above

Question 344

Lognormal

Question

MCQ▾

Suppose that the income of a randomly chosen person in a certain population (in $ 1000 units) has the lognormal distribution with parameters μ = 2 and σ = 1. Find the value of .

Choices

Choice (4)Response

a.

8.5063

b.

12.1825

c.

6.1255

d.

All of the above

Question 345

Joint and Marginal Distributions

Question

MCQ▾

Suppose that and are independent continuous random variables with the following density functions:

for and

What is the value of ?

Choices

Choice (4)Response

a.

b.

c.

d.

Question 346

Distributions of Functions of Random Variables

Question

MCQ▾

Let be a random variable with support and distribution function

Then the distribution function of is ________.

Choices

Choice (4)Response

a.

b.

c.

d.

All of the above

Question 347

With Probability One

Question

MCQ▾

If in probability, then there exists a subsequence of such that ________.

Choices

Choice (4)Response

a.

as with probability 1.

b.

in the -th mean

c.

almost everywhere

d.

Question does not provide sufficient data or is vague