Questions with Complete Solutions - Hamro CSIT

A factory produces two types of electric lamps A and B, in an experiment relating their life, the following results were obtained:

Length of life in 1000 hours 4-6 6-8 8-10 10-12

Number of lamps A 7 9 11 3

Number of lamps B 5 10 13 2

State (i) which model has a longer average life?
(ii) Which model is more consistent in terms of life?

Not Answered Second Semester Asked on 2081 Exam

What are the measures of central tendency? The following are the marks obtained by 95 students in Statistics.

Marks 20-30 30-40 40-50 50-60 60-70 70-80

No. of students 10 17 19 26 15 8

Find:
(i) the modal marks
(ii) the lowest marks of the top 10% student.

Not Answered Second Semester Asked on 2081 Exam

Define statistics. Discuss in brief importance and limitations of statistics.

Not Answered Second Semester Asked on 2081 Exam

What is the significance of normal probability distribution? What are the main properties of normal curve? The time it takes a cell to divide (called mitosis) is normally distributed with an average time of one hour and standard deviation of 4 minutes.

(i) What is the probability that a cell divides in less than 55 minutes?
(ii) What is the time that it takes approximately 99% of all the cells to complete mitosis?

Not Answered Second Semester Asked on 2081 Exam

Define positive and negative correlation. What are the required assumptions for correlation analysis? A data analytic company wants to find the relation between traffic in website (X) per day and server downtime (Y) in minutes per day. The collected data are:

X 9 10 12 9 10 13 13 19

Y 26 38 27 45 55 80 84 100

(i) Find the correlation coefficient between x and y. Interpret the value.
(ii) Find the regression equation of y on x. Estimate the value of y when x = 16.
(iii) Interpret the value of y-intercept and slope of the line.

Not Answered Second Semester Asked on 2081 Exam

What do you mean by dispersion? Distinguish between absolute and relative measures of dispersion. Ten typists applying for a job in a company made the following scores in a typing speed test.

Applicants 1 2 3 4 5 6 7 8 9 10

Speed (word/min) 55 56 80 71 87 62 76 90 73 68

Compute mean, median, range and standard deviation of above data.

Not Answered Second Semester Asked on 2081 Exam

Show that \[
(\mathbb{Q}, +, \cdot)
\] forms a ring.

Not Answered Mathematics II Asked on 2081 Exam

Prove that the binary operation defined on by letting
\[
m \ast n = m + n + 1
\]
is commutative and associative.

Not Answered Mathematics II Asked on 2081 Exam

Determine the least squares error in the least-square solution of , where \[
A = \begin{bmatrix} 4 & 0 \\ 0 & 2 \\ 1 & 1 \end{bmatrix}, \quad
x = \begin{bmatrix} 1 \\ 2 \end{bmatrix}, \quad
b = \begin{bmatrix} 2 \\ 0 \\ 1 \end{bmatrix}
\]

Not Answered Mathematics II Asked on 2081 Exam

Let \[
A = \begin{bmatrix} 1 & 6 \\ 5 & 2 \end{bmatrix}
\] Find the eigenvalues and eigenvectors of $A$ .

Not Answered Mathematics II Asked on 2081 Exam

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