Tribhuvan University

Institute of Science and Technology

2078

Bachelor Level / second-semester / Science

Computer Science and Information Technology( STA164 )

Statistics I

Full Marks: 60 + 20 + 20

Pass Marks: 24 + 8 + 8

Time: 3 Hours

Candidates are required to give their answers in their own words as far as practicable.

The figures in the margin indicate full marks.

**Group A**

**Attempts any TWO questions**

1

What are different methods of measuring dispersion. Sample of polythene bags from two manufactures, A, B, are tested by a prospective buyer for bursting pressure and the results are as follows.

Bursting Pressure | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | |

Number of bags manufactured by | A | 2 | 9 | 29 | 54 | 11 | 5 |

B | 9 | 11 | 18 | 32 | 27 | 13 |

Which set of bags has more uniform pressure? If price are the same, Which manufacture’s bags would be preferred by buyer? Use appropriate statistical tool

2

Write the properties of correlation coefficient. The time it takes to transmit a file always depends on the file size. Suppose you transmitted 30 files, with the average size of 126 Kbytes and the standard deviation of 35 Kbytes. The average transmitted time was 0.04 seconds with the standard deviation 0.01 seconds. The correlation coefficient between the time and size was 0.86. Based on these data, fit a linear regression model and predict the time it take to transmit a 400Kbyte file.

3

- What do you understand by Poisson distribution? What are its main features?
- What do you mean by joint probability distribution function? Write down its properties.

**Group B**

**Attempts any EIGHT questions**

4

If 50 image of your website, 10 have black and white image, and their average scanned image occupies with 2.5 megabytes of memory. The total image occupies by the entire work 281 megabytes. Find the average occupies megabytes of those color images.

5

Calculate Q_{1}, D_{7} and P_{58} from the following data and interpret the results.

Weight | 0-10 | 10-15 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-60 |

No, of person | 4 | 8 | 30 | 15 | 13 | 6 | 4 | 4 | 1 |

6

The following join probability data apply to fatigue test to run on bronze strips. X represent to failure (in 10^{5}) when alternate strips are bent at a high level of deflection. Y represent the same at a lower deflection level.

X/Y | 20 | 30 | 40 | 50 |

4 | 0.01 | 0.03 | 0.05 | 0.02 |

5 | 0.03 | 0.1 | 0.08 | 0.04 |

6 | 0.02 | 0.08 | 0.12 | 0.11 |

7 | 0.02 | 0.04 | 0.07 | 0.18 |

- Find the marginal probability distribution for X and Y
- Determine the conditional probability distribution of Y gives X = 5
- Are x and Y independent

7

Fit a binomial distribution of the following data

X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

f | 5 | 8 | 15 | 14 | 10 | 6 | 2 |

8

If two random variables have the joint probability density function

\(f(x, y) = \left\{\begin{matrix}k(2x + 3y), \enspace for \enspace 0 \leq x \leq 1, \enspace 0 \leq y \leq 1 \\ 0, otherwise\end{matrix}\right.\)

Find (i) constant k (ii) conditional probability density function of X (iii) Identify whether X and Y are independent.

9

Compute first four moments about arbitrary point 4 from following distribution and describe the characteristics of data

X | 2 | 3 | 4 | 5 | 6 |

f | 1 | 3 | 7 | 2 | 1 |

10

The lifetime of a certain electronic component is a normal random variate with the expectation of 5000 hours and a standard deviation of 100 hours. Compute the probabilities under the following conditions

- Lifetime of components between 3000 to 6500 hours
- Lifetime of components between 3000 t0 6500 hours
- Lifetime of components more than 6000 hours

11

Calculate Spearman’s rank correlation coefficient for the following ranks given by three judges in a music contest.

1^{st}Judge |
2 | 1 | 4 | 6 | 5 | 8 | 9 | 10 | 7 | 3 |

2^{nd} Judge |
4 | 3 | 2 | 5 | 1 | 6 | 8 | 9 | 10 | 7 |

3^{rd} Judge |
5 | 8 | 4 | 7 | 10 | 2 | 1 | 6 | 9 | 3 |

Indicate which pair of judges has the nearest approaches to music

12

What do you mean by sampling? Explain the difference between stratified sampling and cluster sampling.

13

State with suitable examples the role played by computer technology in applied statistics and the role of statistics in information technology.

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