# Probability (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 184 - 188 of 205

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## Question number: 184

» Probability » Mathematical Expectation and Conditional Expectation

MCQ▾

### Question

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

### Choices

Choice (4) Response

a.

b.

c.

d.

None of the above

## Question number: 185

» Probability » Moment and Probability Generating Functions

MCQ▾

### Question

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

### Choices

Choice (4) Response

a.

b.

c.

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

### Choices

Choice (4) Response

a.

b.

c.

d.

Question does not provide sufficient data or is vague

## Question number: 188

» Probability » Central Limit Theorems for Independent Variables

MCQ▾

### Question

Suppose that you have a sample of values from a population with mean and standard deviation. What is the probability that the sample mean will be in the interval ?

### Choices

Choice (4) Response

a.

0.1056

b.

0.8944

c.

0.7888

d.

0.2112

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