# ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 308 - 312 of 472

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## Question 308

### Question

MCQ▾

For a standard Beta distribution having pdf , with parameter , which of the following statements is/are correct?

### Choices

Choice (4)Response

a.

If is increasing with mode at

b.

If is increasing with

c.

If is decreasing with mode at

d.

All a., b. and c. are correct

## Question 309

Conditional Distributions

### Question

MCQ▾

Suppose that the joint density of and is

and zero otherwise. Which of the following is equal to

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 310

### Question

MCQ▾

If is the mode of given , then which of the following relation is correct:

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 311

Conditional Distributions

### Question

MCQ▾

A continuous random vector have joint probability distribution function

What is the mean of conditional density of given ?

### Choices

Choice (4)Response

a.

x

b.

c.

d.

None of the above

## Question 312

### Question

MCQ▾

Suppose that a bullet is fired at a target at the origin of a plane coordinate system, with units in meters. The bullet lands at where and are independent and each has the normal distribution with mean 0 and variance 100. The bullet will destroy the target if it lands within 20 meters of the target. Find the probability of this event.

### Choices

Choice (4)Response

a.

b.

0.8647

c.

d.

None of the above