ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 383 - 386 of 454

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 454 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 300.00 or

Question number: 383

» 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: 384

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Suppose that X and Y are independent random variables taking values in N, with probability generating functions P1 and P2 having radii of convergence r1 and r2 , respectively. Then the probability generating function P of X+Y is given by________ for t <r1 r2 .

Choices

Choice (4) Response

a.

P(t)=P1(t)+P2(t)

b.

P(t)=P1(t)P2(t)

c.

P(t)=P1(t)P2(t)

d.

None of the above

Question number: 385

» Probability » Kolmogorov's 0-1 Law

MCQ▾

Question

Consider the random graph we get from the square grid Z2 by keeping each edge with probability p (0 < p < 1 some predetermined constant) IID, and deleting it otherwise (this is percolation on the square grid, and has been extensively studied). Which of the following is correct regarding an infinite connected component somewhere in the graph?

Choices

Choice (4) Response

a.

There always exist finite connected component.

b.

Existence of an infinite connected component is impossible.

c.

Probability that there exists an infinite connected component is 0.5.

d.

None of the above

Question number: 386

» 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

f Page
Sign In