Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 72 - 74 of 109

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Question number: 72

» Probability » Probability Distributions » Lognormal

MCQ▾

Question

Suppose that X has the lognormal distribution with parameters μR and σ(0,) . The distribution of X is a 2-parameter exponential family with natural statistics given by________.

Choices

Choice (4) Response

a.

(ln2(X),exp(X))

b.

(ln2(X),ln(X))

c.

(ln(X),exp(X))

d.

All of the above

Question number: 73

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

X and Y are discrete random variables which are jointly distributed with the following probability function f(x,y):

X and Y are discrete random variables

Finding the correct probability distribution

x

-1

0

1

1

16

19

118

Y

0

19

0

19

-1

118

19

19

What is the value of E[X.Y] ?

Choices

Choice (4) Response

a.

19

b.

118

c.

16

d.

All of the above

Question number: 74

» Probability » Probability Distributions » Lognormal

MCQ▾

Question

Which of the following properties is/are satisfied by the probability density function f(x)forx(0,) of the lognormal distribution with parameters μ and σ .

Choices

Choice (4) Response

a.

f increases and then decreases with mode at x=exp(μσ2).

b.

f is concave upward then downward then upward again, with inflection points at x=exp(μ32σ2±12σσ2+4)

c.

f(x)0 as x0 and as x

d.

All a. , b. and c. are correct

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