ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 342 - 345 of 404

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Question number: 342

» Probability » Probability Distributions » Gamma

MCQ▾

Question

Suppose that X1 and X2 are independent random variables, and that Xi has the gamma distribution with shape parameter ki and scale parameter b for i{1, 2} . Then X1+X2 has the ________distribution with shape parameter________and scale parameter________.

Choices

Choice (4) Response

a.

Gamma, k1+k22,b

b.

Normal, k1+k22,b2

c.

Gamma, k1+k22,b2

d.

None of the above

Question number: 343

» Probability » Probability Distributions » Conditional Distributions

MCQ▾

Question

Suppose that the joint density of X and Y is

f(x,y)=(x+y)4,0<x<y<2

Find the conditional density of Y given X=x .

Choices

Choice (4) Response

a.

2(x+y)4x+43x2

b.

(x+y)4x+43x2

c.

(x+y)4x+4+3x2

d.

2(x+y)4x4+3x2

Question number: 344

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

Continuous random variables X and Y have a joint distribution with density function f(x,y)=π2(sinπ2y)ex for 0<x< and 0<y<1 . Find P[X>1 Y=12].

Choices

Choice (4) Response

a.

e1

b.

π2/4

c.

(π2/4)e1

d.

Question does not provide sufficient data or is vague

Question number: 345

» Probability » Probability Distributions » Gamma

MCQ▾

Question

Three life bulbs has life lengths of X1,X2, and X3 respectively in which all follows an exponential distribution with a mean of 300 hours. Suppose the life length of one bulb is independent of others. Find the probability distribution and expected value for the time until all three bulbs ceases to burn.

Choices

Choice (4) Response

a.

1200 hours

b.

900 hours

c.

600 hours

d.

None of the above

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