Numerical and Statistical Computing-Practice Questions

MCSE-004

Question 1: Obtain the positive root of the equation x2 – 1 = 0 by Regular Falsi method.

Question 2: Apply Gauss – Eliminaiton method to solve the following sets of equation

                  x + 4y – z = -5 ; 

                  x + y – 6z = -12 ;

                  3x –y – z = -4

Question 3: Use method of Lagrange’s interpolation to find f(0.16), for Given function f( x) = sin(x)  where f (0.1) = 0.09983, f (0.2) =0.19867. Also, Find error in f (0.16).

Question 4: Given 𝑑𝑦/𝑑𝑥= y - x, where y(0) = 2. Find y(0.1) and y(0.2), correct to four decimal places, using Runge-Kutta Second Order method.    

Question 5: A farmer buys a quantity of cabbage seeds from a company that claims that approximately 90% of the seeds will germinate if planted properly. If four seeds are planted, what is the probability that exactly two will germinate?  

Question 6: Suppose that the amount of time one spends in a bank to withdraw cash from an evening counter is exponentially distributed with mean ten minutes, that is λ = 1/10. What is the probability that the customer will spend more than 15 minutes in the counter?

Question 7: Compute the approximate derivatives of f(x) = x2 at x = 0.5

for the increasing value of h from 0.01 to 0.03 with a step size of 0.005 using :

(i) first order forward difference model

(ii) first order backward difference model.   

Question 8: Find the root of the equation x3 – x – 1 = 0 lying between 1 and 2 by Bisection method.

Question 9: A problem in statistics is given to the three students A, B and C, whose chances of solving it are ½, ¾, and ¼ respectively. What is the probability that the problem will be solved?

Question 10: A partially destroyed laboratory, the record of an analysis of correlation data, the     following results are legible :

Variance of X = 9 Regression equations:

           8X - 10Y + 66 = 0 ; 

          40X - 18Y - 214 = 0

Find:

        (i) The mean values of X and Y

        (ii) The correlation coefficient between X and Y

        (iii) Standard deviation of Y

 Question 11: An individual's IQ score has a Normal distribution N (100,152).                              Find the probability that an individual IQ score is between 91 and                            121.  

Question 12: What do you mean by term "Goodness to fit test"? What for the said                        test is required?