Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 112 - 114 of 205

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Question number: 112

» 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

Question number: 113

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

If f(x,y)=c(x2+y2) is the density function for the joint distribution of the continuous random variables X and Y defined over the unit square bounded by the points (0, 0),(0, 1),(1, 0) and (1, 1), then the value of c is ________.

Choices

Choice (4) Response
a.

23

b.

32

c.

12

d. None of the above

Question number: 114

» Probability » Probability Distributions » Random Vectors

MCQ▾

Question

The joint density function of two continuous random variables X and Y is

f(x,y)={

What is the value of P(1<X<2, 2<Y<3) ?

Choices

Choice (4) Response
a.

3192

b.

796

c.

5126

d. None of the above

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