Statistical Methods-Bivariate Distributions (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 5 of 5

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Question number: 1

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let (X, Y) be distributed as bivariate normal BVN (3, 1, 16, 25, 3/5). Calculate P (4 < Y < 11.84|X=7)

Explanation

We had known that the conditional distribution of Y given X has mean Equation and variance Equation .

Equation

Equation

Using conditional mean and variance Equation

Equation

Equation

Equation

Equation

Question number: 2

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2014

Essay Question▾

Describe in Detail

The marginal distributions of X and Y are given in the following table:

X

1

2

Total

Y

3

4

?

?

?

?

1/4

3/4

Total

1/2

1/2

1

If the co-variance between X and Y is zero, find the cell probabilities and see whether X and Y are independent.

Explanation

Given that covariance between X and Y is zero

Equation

This gives that f (xy) =f (x) f (y)

So, the joint probability density function of x = 1, y = 3 is

Equation

We know that if the covariance is zero, then the conditional distribution is equal to unknown

… (67 more words) …

Question number: 3

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Let (X, Y) have a joint probability mass function

Equation

= 0, elsewhere

Find the marginal mass functions of X and Y.

Explanation

Let (X, Y) have a joint probability mass function, the individual distribution of either X or Y is called the marginal distribution. So, the marginal mass functions of X is

Equation

and other values of f (x, y) is 0

Equation

Equation

The marginal mass functions of Y is

Equation

… (11 more words) …

Question number: 4

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Given the joint density of (X 1, X 2),

Equation

Find the marginal densities of X 1 and X 2. Also find E [X 1].

Explanation

The joint density is written as

Equation

The marginal distribution of X 1

Equation

Equation

Equation

Equation

Equation

Equation

The marginal distribution of X 2 is

Equation

Equation

Equation

The first integral is

Equation

Equation

So, the marginal distribution of X 2 is

Equation

The mean of X 1 is

… (10 more words) …

Question number: 5

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Show that for discrete distribution β 2 > 1

Explanation

We have to prove that

Equation

By definition of Kurtosis

Equation

Equation

Let x 1, x 2, …, x n are n observations in a set have frequency f 1, f 2, …, f n and the mean of observation is Equation , then

Equation

Assume Equation

… (17 more words) …

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