ISS Statistics Paper I (Old Subjective Pattern): Questions 25 - 29 of 165

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

Question number: 25

» 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: 26

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2009

Essay Question▾

Describe in Detail

A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0.5 at 5 % level of significance?

Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H 0: P = 0.05 against H 1: P < 0.05

Here n = 300, numbers of defectives… (100 more words) …

Question number: 27

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2010

Essay Question▾

Describe in Detail

You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

Company A

Company B

Mean life

1300

1288

Standard deviation

82

93

Sample size

100

100

Which brand of bulbs are you going to purchase if you desire to take a risk of 5%?

Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

Equation

The test statistic is… (80 more words) …

Question number: 28

» Statistical Methods » Measures of Location

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Z be a random variable with p. d. f. f (z). Let z α be its upper α th quantile. Show that if X is

a random variable with p. d. f. Equation then σz α +µ is the upper α th quantile of X.

Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

Equation

X is a random variable with p. d. f. Equation, then quantile is

Equation

Assume Equation

Then the limit is

Lower limit is - Equation and upper… (30 more words) …

Question number: 29

» Probability » Tchebycheffs Inequality

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Show that for 40, 000 throws of a balanced coin, the probability is at least 0.99 that the proportion of heads will fall between 0.475 and 0.525.

Explanation

For balanced coin the probability is p = 0.5. For Bernoulli trails where n = 40, 000, the mean and standard deviation is

Equation

Equation

Using Chebyshev’s inequality,

Equation

The question says that the probability is at least 0.99 that is

Equation

Equation

So, the number of heads comes between… (34 more words) …

f Page
Sign In