Download PTU B-Tech EEE 2020 Dec 5th Sem 70558 Numerical And Statistical Methods Question Paper

Roll No. Total No. of Pages : 03
Total No. of Questions : 18

B.Tech. (Electronics & Electrical Engg.) /

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NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505

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INSTRUCTIONS TO CANDIDATES :

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.

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3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

Do all the questions :

1. Define order of convergence for non-linear equation.
2. Write Newton-cote’s quadrature formula.

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3. Define Eigen value and Eigen vector.
4. What is the difference between the Gauss-elimination and Gauss-Seidel methods?
5. If a random variable ‘X takes the values 1, 2, 3 and 4 such that
   2P (X =1)=3P (X=2)=P (X =3)=5P (X =4), find the probability function of X.
6. Define the condition number.

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7. Write the Newton-Raphson formula for a function f(x) = 0.
8. Define sampling distribution.
9. Write the probability density function for z-distribution.
10. For two lines of regression 7x — 16y + 9 =0 and 5y — 4x — 3 = 0, calculate the coefficient of correlation.

SECTION-B

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11. Perform four iterations of the secant method to find the root of the equation xe^x = cos x correct to four decimal places.
12. Find the largest Eigen value and the corresponding Eigen vector of the matrix

     2 -1 0 -1 2 -1 0 -1 2 

    using Rayleigh’s power method. Take [1, 0, 0]^T as initial Eigen vector.
13. Using Newton’s divided difference formula, find the missing value from the table :

     X 1 2 4 5 6 y 12 15 - 5 - 9 

14. Service calls come to a maintenance center, according to a Poisson process and, on the average, 2.7 calls come per minute. Find the probability that (a) no more than 4 calls come in any minute (b) fewer than 2 calls came in any minute ; (c) more than 10 calls come in a 5-minute period.
15. A continuous random variable X has the following probability density function : f'(x) = A + Bx, 0 1/₂ Find the value of A and B.

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SECTION-C

16. a) Apply Runge-Kutta fourth order method to find the approximate value of y for x =0.2, given that ^dy/_dx =x+y, and y=1 where x=0.
    b) Find by Taylor’s series method, the values of y at x = 0.1 and x = 0.2 to five places of decimals from ^d2y/_dx² = x^dy/_dx—y—1, y(0)=1.
17. For the following data:

     X 1 3 4 8 9 11 14 y 1 2 4 5 7 8 9 

    Obtain :
    a) Regression coefficients of y on x and x on y
    

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    b) Mean of x and y
    c) Coefficient of correlation between x and y.
18. a) A survey of 240 families with 4 children each revealed the following distribution :

     No. of boys 4 3 2 1 0 No. of families 10 55 105 58 12 

    Is the result consistent with the hypothesis that male and female births are equally probable? Use chi-square value for 4 & 5 d.f. at 5% level of significance is 9.49 & 11.07 respectively.
    b) The intelligence quotients (IQ) of 16 students from B.Tech. IInd year showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from B.Tech Ist year showed a mean of 112 and a standard deviation of 8. Is there a significant difference between the IQs of the two groups at significance levels of 0.05? Given that critical value at 28 degree of freedom with 5% level of significance is 2.05.

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

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