BSc IT Sem II 2021 2022 May 2022 NUMERICAL STATISTICAL METHODS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 In floating point representation the number that expressed as a fractional part called
   • a) approximate d) Mantissa
2. Q2 Accuracy and precision are used n context of
3. Q3 Relative error is the ratio between
   • a) Approximate error & Percentage error b) Percentage error and Approximate error
4. Q4 Approximate error is the between the
5. Q5 Bisection method is also called as —
   • a) Bineary search method b) Bracketing method c) Iterative method All the above
6. Q6 Evaluate first iterative value by using Regula falsi method if f(x)
7. Q7 Evaluate ) for first iteration by secant method if f(x) = x — 10 with interval
8. Q8 Find y at x=1.5 if == (—x? — 3x? + 16x 6)
9. Q9 If P=-0.5 ,x=7.5 and Xo = 8 evaluate h =? In Newton interpolation formula
10. Q10 Evaluate X Z if system of equations are X+Y+Z =90 , 2X+3Y+6Z =370 ,3X-8Y-4Z =-340
11. Q11 When n=2 then the method is called
12. Q12 If f(x) 4x+2 dx with n = 6 what is h? by Trapazoidal rule
13. Q14 Area of the right of the ordinate is equal to area of the left of ordinate in normal distribution is
14. Q15 Mean of the distribution in continuous uniform distribution is
15. Q16 If X ~ U(3,12) find mean and variance of continuous uniform distribution
    • a) 7.5and6.75 b) 6.5 and 6.45 c) 5.5and5.35 d) 7.5 and 5.35
16. Q17 Let X be a poisson random variable with P(x=0) =0.2 Find Variance
17. Q18 If byy = 0.45 by, = 0.8 evaluate r= ? =
18. Q19 Any solution of L.P.P. which satisfies the non negativity restrictions of the problem is called
19. Q20 The optimal value of the objective function is attained at the points
    • a) Given by intersection of lines representing inequation with axes only
    • b) Given by intersection of lines representing inequation with X-axis only
    • c) Given by corner points of the feasible region d) At the origin
20. Q2 A) Attempt the following (solve any one ) 4 marks
21. Q1 Define —i) Relative error ii) Percentage error iii) Blunder lv) Truncation error
    • v) Approximate error
22. Q2 The derivative of a function f(x) at a particular value of x can be approximately calculated by f’ (x) = for f(x) = = 0.3find relative true error at X = 2
    • B) Attempt the following (Solve any one) 3
23. Q1 Explain the following - i) Overflow ii) Underflow
    • iii) perform the operation — i) 0.9998E1+0.1000E-99 ii) +0.999E3
24. Q2 Write a short note Conservation law of engineering
25. Q3 A) Attempt the following (Solve any one ) 4 marks
26. Q1 Solve by using Secant method upto three iteration only if f(x) =x
27. Q2 By using Newton -Rapshon method calculate upto four decimal places (Three iteration only) with initial value xy = 3
    • B) Attempt the following (Solve any one ) 3
28. Q1 Given
29. Q2 Find the missing term in the table
30. Q4 A) Attempt the following (solve any one ) 4 marks
31. Q1 Use Gauss Jordan method to solve the following equation ‘ 2) Find the integration — 1) .dx using Simpson’s 3/8 th rule using six strips ,
    • B) Attempt the following (Solve any one ) 3
32. Q1 Using Taylor’s series method , for the equation = 3x + y(1) =0 to find the value of y at where h = 0.1 ( upto third order)
33. Q2 Apply Runge -Kutta second order method to find approximate value of y when x = 0.2 given
34. Q5 A) Attempt the following (solve any one ) 4 marks
35. Q1 Solve graphically the following linear programming problem
36. Q2 Fit the equation of straight line with the help of given data
    • B) Attempt the following (Solve any one ) 3
37. Q1 Two spare parts X and Y are to be produced in a batch .Each me has to go through two processs required in hours per unit and total time available are given below also plot a graph of given L.P.P Profits per unit of X and Y are Rs 5 and Rs 6 .Find how many numbers of spare parts of X and Y are to be produced in this batch to maximize the profit
38. Q2 Find the regression equation Y on X and regression equation X on Y with the help of given data
39. Q6 ) A) Attempt the following (solve any one ) 4 marks
40. Q1 The diameter of electric bulb say X is assumed to be continuous random variable with f (x) = 6x (1 < x <1 determinea number b such that P(X < b) = p(X > b) Also check given function is probability density function
41. Q2 For a random variable X the following data is available ,Evaluate probability mass function, Expected value and variance with the help of given data
    • B) Attempt the following (Solve any one ) 3
42. Q1 Define Binomial distribution , Find binomial distribution if mean =48 and standard deviation is 4 marks
43. Q2 For a binomial variate X , mean is 3 and variance is 2 Find mode of distribution and odds in favour

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