Download PTU B.Tech 2020 March EEE 5th Sem Numerical And Statistical Methods Question Paper

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Roll No. EEEEEEEEEEE Total No. of Pages : 03
Total No. of Questions : 09

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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

1. Do all the questions :
   1. The area of cross-section of a rod is desired upto 0.2% error. How accurately should the diameter be measured?
   2. The mean of the binomial distribution is 20 and standard deviation is 4. Calculate n, q.
   3. Point out the inconsistency, if any, in the following statement “The regression equation of y on x is 2y + 3x = 4 and the correlation coefficient between x and y is 0.8’.

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   4. Write Newton-cote's quadrature formula.
   5. Find the eigen vector corresponding to the eigen value 1 of the matrix

      [1 5]
      [0 4]

   6. If 2 percent of the books bound at a certain bindery have defective bindings. Determine the probability that five of 400 books bound by this bindery will have defective bindings.
   7. What is the difference between the Gauss-elimination and Gauss-Seidel methods.

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   8. Let X be the random variable such that P(X = -2) = P (X =-1), P(X = 2) = P(X=1) and P(X > 0) = P(X < 0) = P(X = 0). Obtain the probability mass function of X and its distribution functions.
   9. Discuss the order of the convergence of the Newton's method for nonlinear equation f(x)=0.
   10. Write the normal equation for the curve y = a + bx, for n points by the method of least squares.

SECTION-B

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1. Perform six iterations of the bisection method to find the root of the equation cos x = xe^x correct to four decimal places.
2. Solve the equations 27x + 6y —z = 85, x + y + 54z = 110, 6x + 15y + 2z = 72 by Gauss-Seidel method.
3. Using Newton's divided difference formula, find the missing value from the table :

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

4. The amount of time, in hours, that a computer functions before breaking down is a continuous random variable with probability density function given by :

   f(x)= Ae^-x ;x>0
   0; x<0

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   What is the probability that a computer will function between 50 and 150 hours before breaking down?

5. A sample analysis of examination results of 500 students was made. It was found that 220 had failed, 170 had secured a third class, 90 was placed in second class and 20 got a first class. Are these figures commensurate with the general examination result which is in a ratio of 4:3:2:1 for the various categories respectively? The table value of chi-square for 3 d.f. at the 5% level of significance is 7.81.

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SECTION-C

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1. 1. Evaluate ? dx / (1+x) from 0 to 6 by using Trapezoidal rule.
   2. 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.
2. 1. Find the coefficient of correlation and obtain the lines of regression from the given data

      X	62	64	65	69	70	71	72	74
      Y	126	125	139	145	165	152	180	208

   2. Samples of sales in similar shops in two rooms are taken for a new product with the following results :

      Town	Mean sales	Variance	Size of samples
      A	57	5.3	5
      B	61	4.8	7

      Is there any evidence of difference in sales in the two towns? Use 5% level of significance for testing this difference between the mean of two samples. Use t_0.05 =2.228

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3. The results of a survey on the sales of a product (Y) as a function of time period (X) are summarized as below :

   	X	Y
   Mean	40	125
   Standard deviation	2.5	16
   Correlation coefficient (r) 0.85

   1. Fit a regression line of Y on X and estimate the value of Y when X is 45.
   2. Fit a regression line of X on Y and estimate the value of X when Y is 135.

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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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