7/28/2019 my asign

1/11

ANS PROBLEM 1:

MATLAB CODE

close all %Close any previously opened window like graph.

clear all %Clear all varibles in workspace.

Trials=2000; %Supposing Number of trials.

for i=1:Trials %Loop

if rand(1,1)

7/28/2019 my asign

2/11

OBSERVATION: From the graph it can be concluded that at least 400 trials are must to getan accurate estimate of probability of heads.

ANS PROBLEM 2(a):MATLAB CODE[THE COMPLETE CONCEPT IS TAKEN FROM THE CODE IN TEXT BOOK]close all; %close previously opened window

clear all; %clear ll variables in workspace

randn('state',0) %initialize guassian random no's gnrtr

x=randn(1000, 1); %generate 1000 random #'s

bincenters=[-4:0.5:4]'; %specify bins center positions

bins=length(bincenters); %total no of bins

h=zeros(bins,1); %Generate 0's vector

for i=1:length(x) %dumping random no's into specified bins

for k=1:bins

7/28/2019 my asign

3/11

if x(i)>bincenters(k)-0.5/2 & x(i)

7/28/2019 my asign

4/11

ANS PROBLEM 2(b):

MATLAB CODE[THE COMPLETE CONCEPT IS TAKEN FROM THE CODE IN TEXT BOOK]close all; %close previously opened wndow

clear all; %clear data in worksapce

randn('state',0) %initialize guassian random number generator

z=randn(2000, 1)+j*randn(2000, 1); %generate complex numbers

Mg_z=sqrt(real(z).^2+imag(z).^2); %magnitude of complex numbers

width_of_PDF=1; %probability density function's width

bincenters=[0.5:0.5:4]'; %specify bins center positions

bins=length(bincenters); %total no of bins

h=zeros(bins,1); %generate 0's vector

for i=1:length(Mg_z) %assigning corresponding values to bins

for k=1 :bins

if Mg_z(i)>bincenters(k)-0.5/2 & Mg_z(i)

7/28/2019 my asign

5/11

h(k,1)=h(k,1)+1;

end

end

end

pxest=h/(1000*0.5); %estimated probability

xaxis=[0:0.01:5]';

px=(xaxis/width_of_PDF).*exp((-0.5*xaxis. 2)/width_of_PDF); %true probability

bar(bincenters,pxest,0.5)

hold on

plot(xaxis,px,'r')

legend('estimated','true')

grid;

title(' Rayleigh PDF . ');

xlabel('complex #s.');

7/28/2019 my asign

6/11

ylabel('Estimated and True Probability');

GRAPH:

ANS PROBLEM 2(c):

MATLAB CODE[THE COMPLETE CONCEPT IS TAKEN FROM THE CODE IN TEXT BOOK]

close all; %close previously opened wndow

clear all; %clear data in worksapce

randn('state',0) %initialize guassian random number generator

z=randn(1000, 1)+j*randn(1000, 1); %generate complex numbers

Mg_z=sqrt(real(z).^2+imag(z).^2); %magnitude of complex numbers

width_of_PDF=1; %probability density function's width

bincenters=[-3:0.5:3]'; %specify bins center positions

bins=length(bincenters); %total no of bins

h=zeros(bins,1); %generate 0's vector

7/28/2019 my asign

7/11

for i=1:length(Mg_z) %assigning corresponding values to bins

for k=1 :bins

if Mg_z(i)>bincenters(k)-0.5/2 & Mg_z(i)

7/28/2019 my asign

8/11

ANS PROBLEM 2(d):

MATLAB CODE[THE COMPLETE CONCEPT IS TAKEN FROM THE CODE IN TEXT BOOK]close all; %close previously opened wndow

clear all; %clear data in worksapce

randn('state',0) %initialize guassian random number generator

z=randn(2000, 1)+j*randn(2000, 1); %generate complex numbers

Mg_z=sqrt(real(z).^2+imag(z).^2); %magnitude of complex numbers

width_of_PDF=1; %probability density function's width

Mag_square=Mg_z.^2; %square of magnitude

bincenters=[0.5:0.5:4]'; %specify bins center positions

bins=length(bincenters); %total no of bins

h=zeros(bins,1); %generate 0's vector

for i=1:length(Mag_square) %assigning corresponding values to bins

for k=1 :bins

7/28/2019 my asign

9/11

if Mag_square(i)>bincenters(k)-0.5/2 & Mag_square(i)

7/28/2019 my asign

10/11

ANS PROBLEM 3:

MATLAB CODE:close all %close previously opened winodw

clear all %clear all data from workspace

randn('state',0)

X1=randn(3e3,1); %3e3 means 3000 random no's

X2=randn(3e3,1);

Y1=X1+(0.1*X2);

Y2=X1+(0.2*X2);

Result=[Y1 Y2];

scatterplot(Result)

title(' Scatter Plot For Y1 and Y2');

xlabel('Y1')

7/28/2019 my asign

11/11

ylabel('Y2')

GRAPH:

Conclusion:

If we let Y1=1 then we can say that Y2 is also approximately equal to 1, because if we

see in the zoomed image of scatterplot in above figure we come to know that for Y1=1, the

values of Y2 on vertical axis lie in the range [0.7,1.2] and the average of this interval is

approximately equal to 1. So our conclusion is right.