What are residual plots? Discuss the utility and disadvantage of residual plots.

Use the Jacobi method to solve the following system of equations: 
3x + 4y + 15z = 54.8
x + 12y + 3z = 39.66
10x + y — 2z = 7.74

Briefly discuss the following with a suitable example:

(i) Non Linear Regression

(ii) Acceptance Rejection method

What are residual plots? Discuss the utility and disadvantage of residual plots.

Solve the following system of equations by using the Gauss Elimination method: (8 Marks)
 x + 2y + z = 3
2x + 3y + 3z = 10
3x y + 2z = 13

Calculate the value of the integral

(i) Simpson's 1/3 rule,

(ii) Simpson's 3/8 rule.

In the table below, the value of y are consecutive terms of a series of which 23.6 is the sixth term. Find the first and tenth terms of the series using Newton’s forward interpolation method.

The length of metallic strips produced by a machine has mean 100 cm and variance 2.25 cm. Only strips with length between 98 and 103 cm are acceptable. What proportion of strips will be acceptable? You may assume that the length of a strip has a Normal Distribution.