# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 147 - 150 of 165

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## Question number: 147

» Probability » Probability Generating Functions

Appeared in Year: 2009

### Describe in Detail

Find the generating function of X whose probability density function is

P [X = r] =pq ^{r-1}, r = 1,2, …, 0 < p < 1, q = 1 - p

### Explanation

The probability generating function is defined as

## Question number: 148

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2015

### Describe in Detail

Given the random samples

X: 1,5, 7,9, 15,17,21,23

Y: 2,6, 10,12,18,20,26,28,32

From the populations having the distribution function respectively as F _{1} and F _{2}, test the hypothesis

against

at 5 % level of significance by the Wald-Wolfowitz run test. It is given that the critical number of runs at the sample sizes (8,9) at 5 % level is 5.

### Explanation

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 8 and sample 2 is Y variables of size m = 9 from two population F _{1} (x) and F _{2} (y) respectively.

The hypothesis under the test is that the null hypothesis is the two population are identical otherwise the alternative is the population is differ.

… (100 more words) …

## Question number: 149

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2010

### Describe in Detail

Find the most likely price in Mumbai corresponding to the price of Rs. 70 at Kolkata from the following:

Kolkata | Mumbai | |

Average price | 65 | 67 |

Standard deviation | 2.5 | 3.5 |

Correlation coefficient between the prices of commodities in the two cities is 0·8.

### Explanation

First we find the regression coefficient β _{YX} where Y is the price at Mumbai and X is the price at Kolkata.

where ρ=0.8, σ _{Y} =3.5, σ _{X} =2.5

The estimated regression equation of Y corresponding to X is

where

… (44 more words) …

## Question number: 150

» Statistical Methods » Measures of Location

Appeared in Year: 2013

### Describe in Detail

For the following frequency distribution on 229 values:

Class | Frequency |

0 - 10 | 12 |

10 - 20 | 30 |

20 - 30 | x |

30 - 40 | 65 |

40 - 50 | y |

50 - 60 | 25 |

60 - 70 | 18 |

the median is found to be 46. Find the values of x and y.

### Explanation

The cumulative frequency is

Class | Frequency | Cumulative frequency |

0 - 10 | 12 | 12 |

10 - 20 | 30 | 42 |

20 - 30 | x | 42 + x |

30 - 40 | 65 | 107 + x |

40 - 50 | y | 107 + x+y |

50 - 60 | 25 | 132 + x+y |

60 - 70 | 18 | 150 + x+y |

Median is 46 which lies in the class 40 - 50. So, median class is 40 - 50.

Here n = 229, l = lower limit of median class = 40

cf = cumulative frequency of the

… (156 more words) …