Name of the College : Karunya Institute of Technology & Sciences
University : Karunya University
Degree : B.Tech
Department : Information Technology
Subject Name : Complex Analysis, Statistics & Z Transforms
Document Type : Question Bank
Website : karunya.edu
Download : https://www.pdfquestion.in/uploads/ka…Transforms.pdf
Karunya Complex Analysis Question Paper
Part – A
Questions :
1. Write the Cauchy Reimann equation in polar coordinates.
2. If the transformation w=f(z) is called fixed points then __________.
3. State Cauchy Integral theorem.
Related : Karunya Institute of Technology & Sciences 09ME248 Industrial Robotics B.Tech Model Question Paper : www.pdfquestion.in/2910.html
4. If z = a is an isolated singularity of f(z) and has an infinite number of Laurent’s terms then it is __________.
5. The moment of coefficient of skewness is defined as __________.
6. State Binomial distribution.
7. Define standard error.
8. The test statistic of F distribution is __________.
9. Find Z{(-1)n}.
10. State whether True/False
11. “ If z[f (t)]= F(z) then z[e-at f (t)]= F[ze-aT ]
12. Prove that w = z2 is analytic
13. Give an example such that u and v are harmonic but u + iv is not analytic.
15. State Cauchy’s residue theorem.
16. Find the mean of Poisson Distribution.
17. What are regression lines?
18. Define Critical region.
19. t and F tests are used only for ____________
20. Find the Z-transform of (n + 1) (n + 2).
21. State the final value theorem in Z-transform.
22. If w = f(z) = u (x,y) + iv(x,y) is analytic, write down the results for f ‘(z).
25. State Cauchy’s residue theorem.
26. Define correlation.
27. Comment on the following : For a binomial distribution mean = 7 and variance =11.
28. What do you mean by level of significance?
29. State the assumptions made for student’s t – test.
30. Find the z-transform of n+2.
31. State the convolution property of z –transform.
32. State the sufficient conditions for the function f(z) = u + iv to be analytic.
33. How many independent conditions are required to determine a bilinear transformation?
34. State Cauchy’s theorem.
36. Define Kurtosis.
37. Comment on the following :
a. For a binomial distribution, mean is 15 and its standard deviation is 5.
38. Define null hypothesis.
39. Mention two uses of c2 – test.
40. Find the Z-transform of an.
41. State the convolution property of z- transform
42. If f(z) is an analytic function with constant modules, then f(z) should be _______.
45. Define isolated singularity.
46. The square root of the product of two regression coefficients gives the value of _______ coefficient.
47. Poisson distribution is the limiting case of _______ distribution.
48. Define null hypothesis.
49. Define level of significance.
50. Define Z – Transform.
52. Define an analytic function.
53. Define invariant points of a bilinear transformation.
54. State Cauchy’s integral theorem.
56. Write Spearman’s rank correlation formula.
57. State the mean and variance of the Poisson distribution.
58. Define Type I error in the testing of hypothesis.
59. Define level of significance.
60. Define Z – transform of a sequence {un}.
61. Fill in the blank : Z (nan) = __________.
62. Write the Cauchy Riemann equations.
64. State Cauchy’s integral theorem.
65. Define Removable singularity.
66. Write the mean and variance of Poisson distribution.
67. Correlation coefficient lies between -1 and +1. (True/False)
68. Define Null hypothesis.
69. Define producers’ risk.
70. Find z (an).
71. State shifting theorem in Z-transform.
Part –B
Questions :
1.Prove that the function u = x3 – 3xy 2 + 3×2 – 3y 2 + 1is harmonic.
3.The ranking of ten students in two subjects A and B are as follows :
A :3 5 8 4 7 10 2 1 6 9
B :6 4 9 8 1 2 3 10 5 7
4.If mean height and standard deviation of height of 200 students of a college are 176.65 and 3.28 respectively, what is the confidence interval of mean height?
5.Find z[et sin 2t]
6. Show that an analytic function with constant real part is constant.
8.Calculate the coefficient of correlation from the following data :
X : 9 8 7 6 5 4 3 2 1
Y : 15 16 14 13 11 12 10 8 9
9. In one sample of 8 observations the sum of the squares of deviations of the sample values from the sample mean was 84.4 and in the other sample of 10 observations it was 102.6. Test whether this difference is significant at 5% level.
11.Show that an analytic function with constant argument is constant.
13. In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution.
14. The means of two simple samples of 1000 and 2000 are 67.5 inches and 68.0 inches respectively. Can the samples be regarded as drawn from the same population of standard deviation 2.5 inches? (Test at 5% level of significance).
18. In a town 10 accidents took place in a span of 50 days. Assuming that the number of accidents per day follows the Poisson distribution, find the probability that there will be three or more accidents in a day.
19. A sample of 400 items is found to have a mean of 67.47. Can it be reasonably regarded as sample from a large population with mean 67.39 and standard deviation 1.30.
20. Find the Z-transform of Cosnq.
22.Expandf(z) = ez in a Taylor’s series about z = 0.
23.The mean of a binomial distribution is 10 and standard deviation 4, calculate n, p, q.
24. If mean height and standard deviation of height of 200 students of a college are 176.65 and 3.28 respectively, what is the confidence interval of mean height?
28. Two lines of regression are 8x – 10y + 66 = 0 and 40x -18y -214 = 0. Find the correlation coefficient of x and y.
29. The means of 2 large samples 1000 and 2000 members are 67.5 inches and 68.0 inches respectively. Can the samples be regarded as drawn from the same population of S.D 2.5 inches?
30.State initial and final value theorems of Z –transform.