Statistical Methods-Bivariate Distributions (ISS 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▾

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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 μY+ρσYσX(xμX) and variance σY2(1ρ2).

E(YX=7)=1+3… (87 more words) …

Question number: 2

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2014

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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

Cov(X,Y)=0E(XY)=E(X)E(Y)

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

So, the joint probability density function of… (168 more words) …

Question number: 3

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2013

Essay Question▾

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

f(x,y)=xy36;x=1, 2,3;y=1, 2,3

= 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

f(x)=P(X=x)=y=13f(x… (121 more words) …

Question number: 4

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

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

f(x1,x2)={18(x12x22)ex1;0<x1<, x2 <x10;otherwise

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

Explanation

The joint density is written as

f(x1,x2)={18(x12x22)ex1;0<x1<,x1<x2<x10;… (395 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

β2>1

By definition of Kurtosis

β2=μ4μ22>1

μ4>μ22

Let x 1, x 2, …, x n are n observations in a set have frequency f 1,… (135 more words) …

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