Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Tribhuwan University

Institute of Science and Technology

2075

Bachelor Level / First Year / Second Semester / Science

B.Sc in Computer Science and Information Technology (STA169)

(Statistics I)

Full Marks: 60

Pass Marks: 24

Time: 3 Hours

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

The figures in the margin indicate full marks.

Section A

Long Answers Questions

Attempt any TWO questions.
[2*10=20]
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 is 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. Which company's computer is more consistent?

$\begin{array}{c|cccccc} \text{Time (in seconds)} & 0\text{-}2 & 2\text{-}4 & 4\text{-}6 & 6\text{-}8 & 8\text{-}10 & 10\text{-}12 \\ \hline A & 5 & 16 & 13 & 7 & 5 & 4 \\ B & 2 & 7 & 12 & 19 & 9 & 1 \\ \end{array}$
[10]
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.(i) Identify which one is response variable, and fit a simple regression line, assuming that the relationship between them is linear.(ii) Interpret the regression coefficient with reference to your problem.(iii) Obtain coefficient of determination, and interpret this.(iv) Based on the fitted model in (a), predict the shear resistance for a normal stress of 30 kilogram per square centimeter.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Normal stress} & 26 & 25 & 28 & 23 & 27 & 23 & 24 & 28 & 26 \\ \hline \text{Shear Stress} & 22 & 27 & 24 & 27 & 23 & 25 & 26 & 22 & 21 \\ \hline \end{array}$
[10]
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.[10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
Measurement of computer chip's thickness (in nanometers) is recorded below. Find the mode of thickness of computer chips and interpret the result.

$\begin{array}{c|ccccc|c} \text{Thickness of chips in n.m.} & 34\text{-}39 & 39\text{-}44 & 44\text{-}49 & 49\text{-}54 & 54\text{-}59 & \text{Total} \\ \text{No. of computers} & 3 & 11 & 16 & 25 & 5 & 60 \end{array}$
[5]
5.
Calculate Q3, D6 and P80 from the following data and interpret the results.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Respiratory rate} & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\ \hline \text{No. of Person} & 8 & 12 & 36 & 25 & 28 & 18 & 9 & 12 & 6 \\ \hline \end{array}$
[5]
6.
Define a random variable. For the following bi-variant probability distribution of X and Y, find (i) marginal probability mass function of X and Y, (ii) p(x $ \le $ 1, y = 2), (iii) P(x $ \le $ 1)

$\begin{array}{c|cccccc} X\backslash Y & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 0 & 0 & 0 & 1/32 & 2/32 & 2/32 & 3/32 \\ 1 & 1/16 & 1/16 & 1/8 & 1/8 & 1/8 & 1/8 \\ 2 & 1/32 & 1/32 & 1/64 & 1/64 & 1/64 & 1/64 \\ \end{array}$
[5]
7.
If two random variables have the joint probability density function Find (i) constant (ii) conditional Probability density function of X given Y (iii) Var (3X + 2Y).

$f(x, y) = \begin{cases} k e^{-(x+y)}, & 0 < x < \infty, 0 < y < \infty \\ 0, & \text{otherwise} \end{cases}$
[5]
8.
A certain machine makes electrical resistors having a mean resistance of 40 ohms and standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution.(i) What percentage of resistors will have a resistance exceeding 43 ohms?(ii) What percentage of resistors will have a resistance between 30 ohms to 45 ohms? [5]
9.
As part of study of the psychological correlates of success in athletes, the following measurements are obtained from members of Nepal national football team. Calculate Spearman's rank correlation coefficient.

$\begin{array}{c|ccccccccc} \text{Anger} & 6 & 7 & 5 & 21 & 13 & 5 & 13 & 14 \\ \text{Vigor} & 30 & 23 & 29 & 22 & 19 & 19 & 28 & 19 \end{array}$
[5]
10.
Compute percentile coefficient of kurtosis from the following data and interpret the result.

$\begin{array}{c|cccccc} \text{Hourly wages (Rs)} & 23\text{-}27 & 28\text{-}32 & 33\text{-}37 & 38\text{-}42 & 43\text{-}47 & 48\text{-}52 \\ \text{Number of workers} & 22 & 16 & 9 & 4 & 3 & 1 \end{array}$
[5]
11.
Write the properties of Poisson distribution. Fit a Poisson distribution and find the expected frequencies.

$\begin{array}{c|cccccccc} \text{X} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \text{Y} & 71 & 112 & 117 & 57 & 27 & 11 & 3 & 1 \end{array}$
[5]
12.
Define primary data and secondary data and explain the difference between them. [5]
13.
What do you mean by sampling? Explain non probability sampling with merits and demerits. [5]