Download PTU B-Tech EEE 2020 Dec 6th Sem 72790 Numerical And Statistical Methods Question Paper

FirstRanker.com

Firstranker's choice

FirstRanker.com

--- Content provided by​ FirstRanker.com ---

Roll No. Total No. of Pages : 03

Total No. of Questions : 18

B.Tech. (EE) PT (Sem.-6)

NUMERICAL & STATISTICAL METHODS

--- Content provided by FirstRanker.com ---

Subject Code : BTEE-505

M.Code : 72790

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

--- Content provided by‍ FirstRanker.com ---

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

1. Define relative error and give bound on the relative error of a floating point number in case of rounding and chopping.

--- Content provided by FirstRanker.com ---

2. Find the polynomial f(x) by using Lagrange's formula for the following data:
   

   x	0	1	2	3
   f(x)	1	3	9	31

3. Define Order of convergence and give order of convergence of Bisection method.
4. Obtain the approximate value of y(0.1) for the initial value problem y' = 1 + y³, y(0) = 1 with step size h = 0.1 by using Taylor series second order method.
5. Evaluate the following integral ?₀³ (5 / (x²+1)) dx using Simpson's 1/3rd rule with three sub intervals.

--- Content provided by⁠ FirstRanker.com ---

6. A Random variable has the following probability distribution:
   

   x	0	1	2	3	4
   P(x)	0	K	2K	2K	7K

   
   Find K.
7. If X is random variable then prove that E(aX + b) = aE(X) + b, where E(X) is mathematical expectation of X.
8. If X is uniformly distributed with mean 1 and variance 1/3 then find P(X < 0).

--- Content provided by‍ FirstRanker.com ---

9. Show that mean of Binomial distribution is np, where n is no. of independent trails and p is probability of success of any trail.
10. Give two properties of correlation coefficient.

SECTION-B

1. Use bisection method to find the solution of the equation 3x - e^x = 0 in the interval [1, 2] accurate within 10^-7.
2. Perform four iterations of Gauss-Seidel method using 4-digit rounding arithmetic to solve the system of equations
   

   --- Content provided by⁠ FirstRanker.com ---

   4x₁ + x₂ + x₃ = 2
   x₁ + 5x₂ + 2x₃ = -6
   x₁ + 2x₂ + 3x₃ = -6
   by taking initial approximation x⁽⁰⁾ = [0.5, -0.5, -0.5]^T.
3. Determine the largest eigenvalue and the corresponding eigenvector of the matrix
   

   --- Content provided by‌ FirstRanker.com ---

   -15	4	3
   10	-12	6
   20	-4	2

   
   correct to three decimal places using the power method.
4. Evaluate the following integral ?₀² (x / (x² +2x+10)) dx using Simpson's 1/3rd rule with four sub intervals. Compare with the exact solution.
5. A random sample of 10 boys had following I.Q.'s: 70, 120, 110, 101, 88, 83, 95, 98, 107, 100. Do these data support the assumption of a population mean I.Q. of 100? Find a reasonable range in which most of the mean I.Q. values of samples of 10 boys lie. (Given t_0.05 = 2.262 for 9 degree of freedom).

SECTION-C

--- Content provided by​ FirstRanker.com ---

1. Use Runge Kutta method of fourth order to approximate y(0.2) taking step size h = 0.1 for the initial value problem dy/dx = -y + e^x, y(0) = 0.
2. A continuous random variable X has the density function
   f(x) = { x²/3, -1 < x < 2; 0, elsewhere }
   a) Verify that f(x) is a density function.
   b) Find P(0 < x < 1).
   

   --- Content provided by​ FirstRanker.com ---

   c) Find the cumulative distribution function F(x).
3. By using the method of least squares, fit a curve of the form y = ax^b to the following data:
   

   x	27	8	62.1	110	161

NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any paper of Answer Sheet will lead to UMC against the Student.

FirstRanker.com

--- Content provided by‍ FirstRanker.com ---