Tribhuvan University

Institute of Science and Technology

2075

Bachelor Level / second-semester / Science

Computer Science and Information Technology( STA169 )

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

Distinguish between absolute and relative measure of dispersion. Two computer manufacturers A and B compete for profitable and prestigious contract. In their rivalry, each claim that their computer a consistent. For this it was decided to start execution of the same program simultaneously on 50 computers of each company and recorded the time as given below.

Time (in seconds) | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | |

Nature of computers manufactured by | A | 5 | 16 | 13 | 7 | 5 | 4 |

B | 2 | 7 | 12 | 19 | 9 | 1 |

Which company’s computer is more consistent?

2

In a certain type of metal test specimen. the effect of normal stress on a specimen is known to be functionally related to shear resistance. The following table gives the data on the two variables.

Normal stress | 26 | 25 | 28 | 23 | 27 | 23 | 24 | 28 | 26 |

Shear Stress | 22 | 27 | 24 | 27 | 23 | 25 | 26 | 22 | 21 |

- Identify which one is response variable, and fit a simple regression line, assuming that the relationship between them is linear.
- Interpret the regression coefficient with reference to your problem.
- Obtain the coefficient of determination, and interpret this.
- Based on the fitted model in (a), predict the shear resistance for normal stress of 30 kilogram per square centimeter .

3

- What do you understand by binomial distribution? What are its main features?
- What do you mean by marginal probability distribution? Write down its properties.

**Group B**

**Attempts any EIGHT questions**

4

Measurement of computer chip’s thickness (in monometers) is recorded below.

Thickness of chips (in nanometers) | 34-39 | 39-44 | 44-49 | 49-54 | 54-59 | Total |

Number of computers | 3 | 11 | 16 | 25 | 5 | 60 |

Find the mode of thickness of computer chips and interpret the result.

5

Calculate Q_{3}, D_{6}, and P_{80} from the following data and interpret the results.

Respiratory rate | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

No. of Person | 8 | 12 | 36 | 25 | 28 | 18 | 9 | 12 | 6 |

6

Define a random variable. For the following bi-variants probability distribution of X and Y , find

- marginal probability mass function of X and Y ,
- P(x≤1, Y=2),
- P(X≤1)

X/Y | 1 | 2 | 3 | 4 | 5 | 6 |

0 | 0 | 0 | 1/32 | 2/32 | 2/32 | 3/32 |

1 | 1/16 | 1/16 | 1/8 | 1/8 | 1/8 | 1/8 |

2 | 1/32 | 1/32 | 1/64 | 1/64 | 1/64 | 1/64 |

7

If two random variables have the joint probability density function

\(f(x, y) = \left\{\begin{matrix}Ke^{-(x+y)}, \enspace 0 < x < ∞, \enspace 0 < y < ∞\\ 0, otherwise\end{matrix}\right.\)

Find (i) constant k (ii) Conditional probability density function of X and given Y (iii) Var(3X + 2Y)

8

A certain machine makes electrical resistors having mean resistance of 40 ohms and standard deviations of 2 ohms. Assuming that the resistance follows a normal distribution.

- What percentage of resistors will have a resistance exceeding 43 ohms?
- What percentage of registers will have a resistance between 30 ohms to 45 ohms?

9

As part of the study of the psychobiological correlates of success in athletes, the following measurements are obtained from members of Nepal national football team.

Anger | 6 | 7 | 5 | 21 | 13 | 5 | 13 | 14 |

Vigor | 30 | 23 | 29 | 22 | 19 | 19 | 28 | 19 |

Calculate Spearman’s rank correlation coefficient.

10

Compute percentile coefficient of kurtosis from the following data and interpret the result.

Hourly wages (Rs) | 23-27 | 28-32 | 33-37 | 38-42 | 43-47 | 48-52 |

Number of workers | 22 | 16 | 9 | 4 | 3 | 1 |

11

Write the properties of Poisson distribution. Fit a poison distribution and find the expected frequencies.

X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Y | 71 | 112 | 117 | 57 | 27 | 11 | 3 | 1 |

12

Define primary data and secondary data and explain the difference between them.

13

What do you mean by sampling? Explain non probability sampling with merits and demerits.

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