Applied Mathematics for Electrical Engineering — Summer 2021

Find a root of the equation x4 – x – 10 = 0 correct to three decimal places, using the bisection method.

By Simpson’s one-third rule, determine the area bounded by the given curve and X-axis between x = 25 to x =25.6 from the data given below. x 25 25.1 25.2 25.3 25.4 25.5 25.6 y 3.205 3.217 3.232 3.245 3.256 3.268 3.280

Apply the method of least squares to determine the constants a and b such that y = a ebx fits the following data: X 0 0.5 1 1.5 2 2.5 Y 0.10 0.45 2.15 9.15 40.35 180.75

Define conditional probability. Abag contains 19 tickets numbered from 1 to 19. Two tickets are drawn successively without replacement. Find the probability that both tickets will show even number?

The following are scores of two batsmen Aand Bin a series of innings: A: 12 115 6 73 7 19 119 36 84 29 B: 47 12 16 42 4 51 37 48 13 0 Who is the better score getter? Who is more consistent?

Discuss Newton-Rapshon method to solve non-linear equation f (x) = 0 numerically. Also, derive the formula to find the cube root of a positive number Nand hence compute3 65.

Discuss the fixed point iteration method. And using it find the real root of x3 – 5x + 3 = 0 starting with x = 0.5 correct to four decimal places.0 1.3

Evaluate ex2 dx by using Simpson’s one-third rule taking h = 0.1. 0.5

Explain the method of least squares in brief. Use it to derive normal equations to fit a straight line y = ax + b.

Newton’s interpolation formulas to find y at x = 0.11 and x = 0.27 from the data given below. x 0.10 0.15 0.20 0.25 0.30 y 0.1003 0.1511 0.2027 0.2553 0.3093 OR1

Evaluate ex2 dxby 3-point Gaussian quadrature formula.0

Define Central difference operator in terms of .1 Establish the operator relations D = log(1) h

Write Newton’s Divided difference interpolation formula for unequal intervals. Determine the interpolating polynomial of degree three by using Lagrange’s interpolation for the following data. Also find f(2) x – 1 0 1 f(x) 2 1 0 – 1

(i) State Baye’s theorem. (ii) Define Bernoulli’s trials. (iii) Define independent events.

Define probability density function. If the probability density function of a random variable is given by   f(x)k 1x2 ,if 0 x1 0 ,elsewhere Find the value of k and probability that Xtakes the value greater than 0.5

What do you mean by predictor-corrector methods? State names of any three predictor-corrector methods. Apply Milne’s predictor–corrector method to obtain y(2) correct to three decimal places, if y(x) is the solution dy 1   of  x y where y(0) = 2, y(0.5) =2.636, y(1) = 3.595, y (1.5)= dx 4.968

Discuss Binomial probability. The probability a man aged 60 will live to be 70 is 0.65. What is the probability that out of 10 men aged 60 now, at least 7 would live to be 70?

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of the number of kings.

Apply second order Runge-Kutta method to find an approximate value of dy y(0.2) given that  x y2 , y(0) = 1 and h = 0.1. dx

State any four known methods for finding skewness. Apply suitable method to compute the coefficient of skewness from the following figures: 25, 15, 23, 40, 27, 25, 23, 25,

Let Xhas the probability density function1 f(x) for  3 x  323 0 elsewhere3 Find the actual probability P{X– } and compare it with the upper2 bound obtained by Chebyshev’s inequality.

Find kurtosis from the following data. Class 0–10 10–20 20–30 30–40 interval Frequency 1 4 3

What do you mean by kurtosis? Illustrate the shape of three different curves on the basis of value of .2

Abag contains 6 white and 9 black balls. Four balls are drawn at a time. Find the probability for the first draw to give four white balls and second2 draw to give four black balls in each of the following case.

with replacement and (ii) without replacement