# Untitled

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Dec 27th, 2015
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1.
2. close all
3. clear all
4.
5.
6. T = 10000;
7. mu =2 ;
8. sigma = 0.4 ;
9.
10.
11. x = (randn(T,1)* sigma) +mu ; %% X distributed (mean = mu and std = sigma)
12. Z = (x -mu)./sigma ;
13. xPos = 1.5;
14.
15.
16. figure
17. subplot(4,2,1)
18. hist(x)
19. title('a) X')
20. subplot(4,2,2)
21. hist(Z)
22. title('b) Z')
23.
24.
25.
26. subplot(4,2,3)
27. xsort = sort(x);
28. PDF_X = normpdf(xsort,mu,sigma );
29. plot(xsort,PDF_X)
30. title(strcat('c) pdf(X), integral =',num2str( trapz(xsort,PDF_X))))
31. hold on
32. y1=get(gca,'ylim');
33. plot([xPos xPos],y1);
34. hold off
35.
36.
37. subplot(4,2,4)
38. zsort = sort(Z);
39. PDF_Z = normpdf(zsort,0,1 );
40. plot(zsort,PDF_Z)
41. title(strcat('d) pdf(Z), integral =',num2str(trapz(zsort,PDF_Z))))
42. hold on
43. y1=get(gca,'ylim');
44. plot([xPos xPos],y1);
45. hold off
46.
47.
48. subplot(4,2,5)
49.
50. plot(xsort,PDF_Z)
51. title(strcat('e) pdf(Z) wrong domain, integral =',num2str(trapz(xsort,PDF_Z))))
52. hold on
53. y1=get(gca,'ylim');
54. plot([xPos xPos],y1);
55. hold off
56.
57.
58. subplot(4,2,7)
59. PDF3 = PDF_Z./sigma ;
60. plot(xsort,PDF3)
61. title(strcat('f) pdf(Z)/sigma, integral =',num2str(trapz(xsort,PDF3))))
62. hold on
63. y1=get(gca,'ylim');
64. plot([xPos xPos],y1);
65. hold off
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