Applied Mathematics for Electrical Engineering — Winter 2021

Construct the difference table for f(x)(x2)2for x1,2,3and find 2f(3).

Find a real root of the equation x34x90using bisection method in four stages.

Explain Bay’s rule for probability. Three boxes contained 10%, 20% and 30% red colors pens. Apen is selected at random whose color is red. Determine the probability that it came from 3rd box, 2nd box , 1st box.

Prove that (1)(1)1.

dy Using Picard’s method solve  xy2with the initial condition dx y(0)1and compute y(0.1).

6 1 Evaluate  dx for n6 using Simpson’s one third rule and 1x0 Simpson’s three eights rule. Also find an approximate value of log 2. e

dy Using the Runge Kutta method of fourth order solve  xy y2with dx the initial condition y(0)1. Compute y(0.2) by taking h0.1.

x Is f(x) ,x0,1,2,3,4 define probability distribution? Justify your6 answer.

Compute f(9.2) from the following values using Newton’s divided difference formula. x 8 9 9.5 11 f (x) 2.079442 2.197225 2.251292 2.397895

Using the method of least squares, find the best fitting second degree curve to the given following data: x 1 2 3 y 6 11 18 27

For the following distribution, find the value of k. x 1 2 3 4 51 f (x) 0.1 k 0.2 3k 0.3

Using the Euler’s method, find y(0.2) given that dy 2x  y ,y(0)1,h0.1 . dx y

Find the root of the equation xsinxcosx0 using Newton-Raphson method correct to three decimal places.

Find the median of the following data: Marks <20 21-30 31-40 41-50 51-60 61-70 No. of 5 15 20 6 6 Students

Using the Newton forward formula, find the approximate value of f(1.6) , if x 1 1.4 1.8 2.2 f (x) 3.49 4.82 5.96 6.5

The joint probability density function of two continues randon variable X and Yis given by f(x,y)cxy;0 x4,1 y5 0; otherwise Find (a) value of constant c, (b) P(X 3,Y 2),

P(1 X 2,2Y 3).

Find the first four moments of the observation 1,3,5,7,8,9.

Using Langrange’s interpolation formula, find f(3) from the data given: x 1 5 7 f (x) 1.10 2.00 3.23 4.50

Find a real root of the equation xlog x1.2 by using Regula- falsi10 method correct to four decimal places.(or four stages)

1 If Aand Bare independent events, where P(A) ,P(B) .43 Find P(AUB).

2 Compute (1x)dx by a two point Gaussian quadrature formula.0

Find the Karl Pearson’s coefficient of skewness for the following data: Marks 20 21 22 23 24 25 26 27 28 No. of 7 12 25 10 8 6 8 3 1 students

If Aand Bare mutually exclusive events and P(A)0.30,P(B)0.45, then find the probability of the events,

P(A) (b) P(AB) (c) P(AB).

5.2 Evaluate the integration  log xdx using Simpson’s th rule.take e 84 h0.2.

Find the mean, median and mode for the following data: Class 50- 53- 56- 59- 62- 65- 68- 71- 74- Frequency 3 8 14 30 36 28 16 10