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
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?
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 |
Group B
Attempts any EIGHT questions
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.
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 |
Define a random variable. For the following bi-variants probability distribution of X and Y , find
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 |
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)
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.
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.
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 |
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 |
Define primary data and secondary data and explain the difference between them.
What do you mean by sampling? Explain non probability sampling with merits and demerits.