ISS Statistics Paper I (Old Subjective Pattern): Questions 59 - 64 of 165

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Question number: 59

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2010

Essay Question▾

Describe in Detail

For 2X2 table

A

b

C

d

prove that Chi-square test of independence gives

χ2=N(adbc)(a+c)(b+d)(a+b)(c+d),N=a+b+c+d

Explanation

Let the contingent table is

Class

A

α

Total

B

a

b

a + b

β

c

d

c + d

Total

a + c

b + d

a + b + c + d =N

Here A denotes the presence of any attributes and α denotes the absence of… (453 more words) …

Question number: 60

» Probability » Standard Probability Distributions » Uniform

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let X be a random variable with a continuous distribution function F. Show that F (X) has the uniform distribution on (0, 1).

Explanation

Let U = F (x), then the distribution function of G of U is given by

G(u)=P[Uu]=P[F(X)u]=P[XF1(u)]

The… (93 more words) …

Question number: 61

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2012

Essay Question▾

Describe in Detail

For the Cauchy distribution given by

f(x)=kσ2+(xμ)2,<x<

where k is a constant to be suitably chosen, derive the expression for the distribution function. Hence obtain a measure of central tendency and a measure of dispersion. What are the points of inflexion of the distribution?

Explanation

We choose k as constant that gives the integral over the range x for the density function is equal to one.

kσ2+(xμ)2dx=1

kσ[tan1(xμσ… (381 more words) …

Question number: 62

» Probability » Sample Space

Appeared in Year: 2011

Essay Question▾

Describe in Detail

A fair die is thrown until a 6 appears. Specify the sample space. What is the probability that it must be thrown at least 3 times?

Explanation

A fair die content the value {1, 2, 3, 4, 5, 6}

So, the probability of getting 6 is p = 1/6, then probability of getting other than 6 is q = 5/6

If we throw a die, the six is appear. Then the probability is p and the experiment… (162 more words) …

Question number: 63

» Probability » Conditional Probability

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Consider the following bivariate p. m. f. of (X, Y):

p (0, 10) = p (0, 20) = 2/18;

p (l, 10) = p (l, 30) = 3/18;

p (1, 20) = p (2, 30) = 4/18;

Obtain the conditional mass functions p (y lx = 2), and p (y lx = 1).

Explanation

The joint probability is given

-

x

Total

-

0

1

2

Y

10

2/18

3/18

0

5/18

20

2/18

4/18

0

6/18

30

0

3/18

4/18

7/18

Total

4/18

10/18

4/18

1

First find the marginal probability of x at x = 0, 1, 2

p(x)… (136 more words) …

Question number: 64

» 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

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) …

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