ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 110 - 114 of 165

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Question number: 110

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

Essay Question▾

Describe in Detail

For 20 pairs of heights of father (X) and son (Y) measured in cm, the following data are obtained:

Equation

Test whether the cut on the X-axis can be assumed to be zero, at 5 % level of significance.

Explanation

In the regression model, the cut on the X-axis can be assumed to be zero means the intercept zero. The test of the hypothesis is

Equation

Can be tested by the statistic is

Equation

where Equation is the standard error of an estimator b 0.

Equation

Equation

where

Equation

… (32 more words) …

Question number: 111

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Let X have the density function,

Equation

(i) Find the constant c.

(ii) Find the distribution function.

(iii) Compute P [X > -1/2].

Explanation

(I) To find the value of c using this density function, the integral of density is equal to one by probability definition. The range of X is|X| < 1

Equation

when X is positive, | X|=X < 1 and X is negative, | X|=-X < 1 that is X >

… (21 more words) …

Question number: 112

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Write down the probability mass function of geometric distribution. State and prove its ‘lack of memory property’. Find also the mean and the variance of the distribution.

Explanation

If there are number of trails such that the probability of success is p. So, the probability that there are x failures before the first success is

Equation

This is the probability mass function of geometric distribution

Statement:

Among the all discrete distributions, the geometric distribution has the lack of

… (169 more words) …

Question number: 113

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

Essay Question▾

Describe in Detail

125out of 285 college-going male students in 1995 from a city were found to be smokers. Another sample of 325 such students from the same city in 2012 included 95 smokers. Examine at 5 % level of significance if smoking habit among college-going students is on the decrease in this city.

Explanation

The given information can be written as in a table:

Year

Smoker

Non-smoker

Total

1995

125

160

285

2012

95

230

325

Total

220

390

610

Here, the null hypothesis is that the proportion of smoker in this two year is same and the alternative is there is decrease in

… (98 more words) …

Question number: 114

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2014

Essay Question▾

Describe in Detail

If f x (x) be the probability density function of a N (µ, σ 2) distribution, then show that

Equation

where Equation , Equation and φ (x) and Φ (x) are the probability density function and distribution function of the standard normal distribution respectively.

Explanation

Given that f X (x) be the probability density function follows N (µ, σ 2).

Equation

Then

Equation ………. (1)

Let assume that Equation =z, then differentiate Equation

The limit is also change, the lower limit is Equation and upper limit is Equation

Equation (1) can be written as

… (15 more words) …

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