Tribhuvan University

Institute of Science and Technology

2075

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

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
  1. Identify which one is response variable, and fit a simple regression line, assuming that the relationship between them is linear.
  2. Interpret the regression coefficient with reference to your problem.
  3. Obtain the coefficient of determination, and interpret this.
  4. Based on the fitted model in (a), predict the shear resistance for normal stress of 30 kilogram per square centimeter .
3
  1. What do you understand by binomial distribution? What are its main features?
  2. 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 Q3, D6, and P80 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

  1. marginal probability mass function of X and Y ,
  2. P(x≤1, Y=2),
  3. 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.

  1. What percentage of resistors will have a resistance exceeding 43 ohms?
  2. 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.