Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 120 - 122 of 205

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Question number: 120

» Probability » Probability Distributions » Conditional Distributions

MCQ▾

Question

A continuous random vector (X,Y) have joint probability distribution function

f(x,y)=ey,0<x<y<

What is the mean of conditional density of Y given X=x ?

Choices

Choice (4) Response

a.

1x

b.

1+x2

c.

x

d.

None of the above

Question number: 121

» Probability » Probability Distributions » Gamma

MCQ▾

Question

Suppose that a bullet is fired at a target at the origin of a plane coordinate system, with units in meters. The bullet lands at (X,Y) where X and Y are independent and each has the normal distribution with mean 0 and variance 100. The bullet will destroy the target if it lands within 20 meters of the target. Find the probability of this event.

Choices

Choice (4) Response

a.

0.8647

b.

0.5233

c.

0.2186

d.

None of the above

Question number: 122

» Probability » Probability Distributions » Lognormal

MCQ▾

Question

Using the method of moment estimation, find the estimators μ~ and σ~2 of parameters of X if X~Lognormal(μ,σ2) .

Choices

Choice (4) Response

a.

μ~=ln(i=1nXi)2+2ln(i=1nXi2)32ln(n) and σ~2=ln(i=1nXi)2ln(i=1nXi2)+ln(n)

b.

μ~=ln(i=1nXi2)ln(i=1nXi)12ln(n) and σ~2=ln(i=1nXi2)+2ln(i=1nXi2)+ln(n)2

c.

μ~=ln(i=1nXi2)2+2ln(i=1nXi)32ln(n) and σ~2=ln(i=1nXi2)2ln(i=1nXi)+ln(n)

d.

All of the above

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