Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 184 - 187 of 205

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 469 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: 184

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

If Equation is the number of points rolled with a balanced die, find the expected value of Equation .

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

None of the above

Question number: 185

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Suppose that Equation and Equation are independent random variables taking values in N, with probability generating functions Equation and Equation having radii of convergence Equation and Equation , respectively. Then the probability generating function Equation of Equation is given by________ for Equation Equation .

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

None of the above

Question number: 186

» Probability » Kolmogorov's 0-1 Law

MCQ▾

Question

Consider the random graph we get from the square grid Equation 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: 187

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

Question

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

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Question does not provide sufficient data or is vague

f Page
Sign In