Statistics I TU Board 2075 question paper

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

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 .

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.

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 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

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

If two random variables have the joint probability density function

$f(x,y)=\{\begin{array}{c}K{e}^{-(x+y)},0<x<\infty ,0<y<\infty \\ 0,otherwise\end{array}$

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.

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?

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.