# 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

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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:

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

Can be tested by the statistic is

where is the standard error of an estimator b 0.

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## Question number: 111

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Let X have the density function,

(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

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

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## Question number: 112

» Probability » Standard Probability Distributions » Geometric

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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

This is the probability mass function of geometric distribution

Statement:

Among the all discrete distributions, the geometric distribu

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## Question number: 113

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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 the smoker

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## Question number: 114

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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

where , 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).

Then

………. (1)

Let assume that

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