ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 308 - 310 of 458

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Question number: 308

» Probability » Probability Distributions » Lognormal

MCQ▾

Question

Suppose that X has the lognormal distribution with parameters μ∈R 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: 309

» 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: 310

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Suppose that (X1,X2,…) is a sequence of random variables (defined on the same probability space) and that the distribution of Xn converges to the distribution of the constant casn→∞ . Then________.

Choices

Choice (4) Response

a.

Xn→c as n→∞ k -th mean

b.

Xn→c almost everywhere

c.

Xn→c as n→∞ in probability

d.

All of the above

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