Calculate the value of the integral

(i) Simpson's 1/3 rule,

(ii) Simpson's 3/8 rule.

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.

A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 18 and that of wife’s selection is ¼. What is the probability that:
(i) Both of them will be selected
(ii) Only one of them will be selected
(iii) None of them will be selected.

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

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.

Use Regula-Falsi method to find the roots of the equation f(x) =x³ + x – 1.

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.