# ISS 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

### 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

… (199 more words) …

## Question number: 111

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2013

### 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

… (224 more words) …

## Question number: 112

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2012

### 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… (555 more words) …

## Question number: 113

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

### 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… (199 more words) …

## Question number: 114

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2014

### 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

… (216 more words) …