Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 26 - 27 of 109

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Question number: 26

» Probability » Probability Distributions » Rectangular

MCQ▾

Question

An n-dimensional rectangular box with sides X1,X2,,Xn is to be constructed. The volume is Vn=i=1nXi . The edge-length l of an n-cube with the same volume as the random box is l=Vn1/n . Let X1,X2,,Xn be i. i. d. uniform random variables over the interval [0,a]. Which of the following statements is/are correct regarding this?

Statements:

1) Expected edge length captures the idea of the volume of the box.

2) Expected edge length does not captures the idea of the volume of the box.

3) limnVn1/n<a2

Choices

Choice (4) Response

a.

1 and 3

b.

3

c.

2 and 3

d.

Question does not provide sufficient data or is vague

Question number: 27

» Probability » Probability Distributions » Multinomial

MCQ▾

Question

If X=(X1,X2,,Xk)~Mult(n,π) where, π=(π1,π2,,πk) then, X*=(X1+X2+X3,X4,Xk)~ ________.

Choices

Choice (4) Response

a.

Bin(n,π)whereπ=(π1+π2+π33+π4++πkn)

b.

Bin(n,π)whereπ=(π1+π2+π33+π4++πk)

c.

Bin(n,π)whereπ=(π1+π2++πk)k

d.

None of the above

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