Probability-Mathematical Expectation and Conditional Expectation (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 5 of 7

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Question number: 1

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let random variables Xk=N(mk,σk2) , k=1,,n be independent normal random variables. So if X=i=inXn then, which of the following is the characteristic function of X if m=i=inmi and σ2=i=inσi2 ?

Choices

Choice (4) Response

a.

eitm+σ2t2

b.

eitmσk2t22

c.

eitmσ2t22

d.

All of the above

Question number: 2

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let X and Y be independent; each is uniformly distributed on [0, 1]. Let Z=X+Y , then E[XZ X]= ________.

Choices

Choice (4) Response

a.

X+12

b.

12

c.

1

d.

X(X+12)

Question number: 3

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

If X is the number of points rolled with a balanced die, find the expected value of g(X)=2X2+1 .

Choices

Choice (4) Response

a.

236

b.

25

c.

13

d.

None of the above

Question number: 4

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let X be an exponential random variable with parameter μ . It’s characteristic function is________.

Choices

Choice (4) Response

a.

μ+itμit

b.

μμ+it

c.

μμit

d.

Question does not provide sufficient data or is vague

Question number: 5

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

Let X,Y,Z be random variables, a,bR and g:RR . Assuming that expectations exist, we have E[X Y] = ________

Choices

Choice (4) Response

a.

E[E[X Y,Z] Y]

b.

E[X Y,g(Y)]

c.

E[X] if X and Y are independent.

d.

All a. , b. and c. are correct

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