Marks of six students are tabulated below:

From the population, tabulated above, you are supposed to choose a sample of size two.

(a) Determine, how many samples of size two are possible

(b) Construct sampling distribution of means by taking samples of size 2 and organize the data.

What are the various probability distributions, give respective formulas of each type of distribution. Now solve the problem“The probability that at least one of the two independent events occurs is 0.5. Probability thatthe first event occurs but not the second is 3/25. Also the probability that the second event occurs but not the first is 8/25.”Find the probability that none of the two events occurs

Write a program that approximates the solution of the initial value problem: y f t y ( , ) with 0 y a y ( ) over [ , ] a b using Euler’s method. Using the program to approximate the solution of the initial value problem:

y '= -2t2 y with y(0) =1

Write a program that approximates the value of a definite integral

using Simpson's 1/3rd rule, with M sample points. Find an approximate value of the integral of 2x ² + x + 5 using the program with 8 intervals over the interval [0, 4

Write a program that approximates the derivative of a given (differentiable) function f (x) at x = x0, using forward difference formula taking only 3 points having value of x as 0, 1 and 2 respectively. Using the program find the derivative of function f(x)=( x ) ^5/2 at x=0.5

Write a program to interpolate using Newton's Backward difference formula using only three points. Solve Problem asked in Question 4 using Newton’s Interpolating polynomial using Backward difference (instead of Lagrangian Polynomial).

Write a program that uses Lagrangian polynomials for interpolation. You must use only three nodes such that the interpolating polynomial is at most quadratic. Using this program find approximate value of f (x) = 5^x at x =1.5. The nodes are at points x 0 = 0, x 1 = 1, x 2 = 2.

Write a program that approximates a root of the equation f (x) = 0 in an interval [a, b] using Newton-Raphson method. The necessary assumptions for application of this method should be explicitly mentioned. Use the method to find smallest positive root of the equation

2x⁴ - 5x² + 10x - 32=0.

Write a program that uses Gauss-Seidel iterative method to solve system of linear equations. Use the method to solve the system of linear equations given in Q. No. 1 above.

Write a program that implements Gaussian elimination method with pivot condensation for solving n linear equations in n variables, that calls procedures

(i) lower-triangularisation and

(ii) back substitutions (codes of procedures are also to be written). Use the program for solving the following system of linear equations:

5x - 7y + 8z = 11

4x - 9y + 3z = 2

9x +2y + 5z = 25

Create four pages for the website viz. Home, Attendance, Results and Feedback; all the four pages should have same Top, Menu, and Develop division but different Content division. The Menu Division should provide links to the Home page as well as all the other three pages. All these four menu options should be available in all the web pages designed by you for this assignment. Thus, this

Menu division may be used for navigating among the four web pages. The Content division of every page should be different. The information that should be displayed in Content Division of each of the pages is described below:

(i) The Home page should display a Welcome Message from the School and list the strengths of the School.

(ii) The Attendance page should display a form for logging into the Database of the School as shown.

(iii)The Results page should display the Results of a student to his/her parents.

(iv) The Feedback page should display a form asking for student name, class, a text area field for writing feedback information and a Submit Button.

(b) Create an external CSS that gives different background colour to each division. You may choose the format of other elements as per your choice.

(c) Create a JavaScript program that generates an error message if Username field is left blank in the form of Attendance page; or if the length of entered password in the password field is less than 6 characters. In case of an error, after displaying the error message, the login form should be displayed again.

(d) Implement the following using jsp program, servlets, java classes, database(s), etc. for the pages as described below:

(i) When a user presses Submit button after properly filling Username and password in the form in the Attendance page, these details are checked in a database, and in case, the entered username and password are correct, the Student Name, Class, days present and days absent are displayed on the screen. You may also create a cookie, if needed, to remember the username and password.

(ii) On selection of Results option, the result of student, whose parents have successfully logged in, is displayed. You may have to use cookies for this purpose.

(iii) When you press the Submit button of the Feedback Form, the information entered in the form should be stored in a database table.

(iv) You must design, create and use a suitable database for the purposes as above.

You may make suitable assumptions, if needed.

Create a website for a School which provides information about student's performance to their parents, who may register to the website. The website should be designed using logical divisions through tags and an external CSS file. Every page of the website should be divided into four divisions namely – Top, Develop, Menu and Content as displayed in the following figure:

Perform the following tasks for the website as given above:

Configure the DHCP server on the Linux operating system . Write all the steps. Sort each column of the table and show the result.

Setup a network connection in Linux. Configure it for Wireless networking. Once the internet connection is established, use netstat and tcptrackcommands and show the results.

Write and run commands in Linux for the following tasks:

- To check if a particular process is running or not

- To see currently running processes and other informations like memory and CPU usages

- List all file names that have a letter h as 4th character in the name

- List all the file names that have the number 2 or 5 in the name

a) Run the following Linux commands on your machine and show the output:

• cat
• sort
• See Answer →

(b) Write the answer to the following queries:

• What type of socket is created?
• What are the arguments used for sending and receiving messages ?

(a) Write and execute a UDP client and a server program in C-language to perform the following tasks and show the result

- The UDP client program sends a string ( in lower case letters) to the UDP server program

- The UDP server program converts the string into upper case letters and then sends it to the client.

How would you introduce yourself in each of these situations given below? 

i You meet a popular motivational speaker in a conference. Introduce yourself.

ii You meet an eminent scientist in a flight journey. Introduce yourself.

Read this telephone conversation and then complete with suitable words.

Assistant: Sales department. Good morning. You: ……………………………………………………….. Assistant: Certainly. What exactly would like to know about our filing cabinets? You: ……………………………………………………….. Assistant: They cost Rs. 9,000 each. You: ……………………………………………………….. Assistant: I am sorry, but they’re not available in black. You: ……………………………………………………….. Assistant: We can deliver by the end of the week. You: ……………………………………………………….. Assistant: You’re welcome. Thank you for calling.