Here is the code developed in software assignment#1: (1) the Matlab code develop
ID: 3583276 • Letter: H
Question
Here is the code developed in software assignment#1: (1) the Matlab code developed in Software Assignment #1: a. Convert the code that generates the random number (H,T) with equal probabilities into a function called myBernolli (p, S) that takes as an input the probability of success p and S is the outcome defined as success (either Tor H) and returns the outcome of the trial (either Tor H). b. Test that your function is actually producing the success outcome with probability p by running the function in a loop of 1000 trials and counting how many times success is produced (it should be close to p 1000). c. Write a Matlab function called myBinomial(n,p) that takes as an input the total number of trials n, the probability of success p and the outcome defined as success S and uses myBernolli0 to retum as an output the number of successes x. d. Write a Matlab function called myG that takes as an input the eometrico probability of success p and the outcome defined as success Sand uses myBernolli to return as an output the number of trials till first success x. e. Verify that myBinomia 0 and myG generates values that follows eometrico Binomial and Geometric Distributions by running each of them 5000 times in a loop and plotting a histogram of the random variable x generated from each. Hints: Random numbers with probability pare generated in Matlab using the command function rando. Read the help on Matlab to know how to use the function by typing help rand in Matlab command line. Histogram plots [hist00 is a function in Matlab. Read its help to know how to produce the requirements in part e.Explanation / Answer
head=0;
tail=0;
for i=1:1000000
x=rand(1);
if x>=0.5
tail=tail+1;
else
head=head+1;
end
end
heads=head/100
tail=tail/100
for 100 trails
heads =
0.5300
tail =
0.4700
For 1000 trails
heads =
4.9000
tail =
5.1000
For 10000 trails
heads =
50.3300
tail =
49.6700
For 100000 trails
heads =
500.1000
tail =
499.9000
From that clearly probabilities are getting closer when number of trails increased.
a)
p=0.1;
function result = mybernoulli(p)
U1 = rand(1); % Generate a sample in Unif(0,1)
if U1 < p
fprintf('the sucess ');
else
fprintf('the failure ');
end
answer:
the success
b)
p=0.1;
c=0;
function result = mybernoulli(p)
for i=1000
U1(i) = rand(1); % Generate a sample in Unif(0,1)
if U1(i) < p
fprintf('the sucess ');
c=c+1;
disp(c);
else
fprintf('the failure ');
end
end
answer:
the sucess
567
c)
function probdf = mybernoli(k,n,p)
m =5000 ;
idxx = 0;
for i=1:m
idxx= idxx+ double(nnz(rand(n,1) < p)==k);
end
probdf = idxx/m;
end
k = 0:5000;
y1_pdf = mybernoli(k,20,0.5);
y1_cdf = cumsum(y1_pdf);
figure;
subplot(1,2,1);
stem(k,y1_pdf);
title('PDF');
subplot(1,2,2);
stairs(k,y1_cdf);
axis([0 20 0 1]);
title('CDF')
d)
function probdf = mygeometri(k,p)
m = 10000;
probdf = zeros(numel(k));
for j=1:numel(k)
idxx = 0;
for i=1:m
idxx = idxx + double(nnz(rand(j,1) < p) < 1);
end
probdf(j) = idxx/m;
end
end
k = 0:5000;
y1_pdf = mygeometri(k,0.5);
y1_cdf = cumsum(y1_pdf);
figure;
subplot(1,2,1);
stem(k,y1_pdf)
title('PDF');
subplot(1,2,2);
stairs(k,y1_cdf);
axis([0 20 0 1]);
title('CDF');
e)
function probdf = mygeometri(k,p)
m = 10000;
probdf = zeros(numel(k));
for j=1:numel(k)
idxx = 0;
for i=1:m
idxx = idxx + double(nnz(rand(j,1) < p) < 1);
end
probdf(j) = idxx/m;
end
end
k = 0:5000;
y1_pdf = mygeometri(k,0.5);
y1_cdf = cumsum(y1_pdf);
figure;
subplot(1,2,1);
stem(k,y1_pdf)
title('PDF');
subplot(1,2,2);
stairs(k,y1_cdf);
axis([0 20 0 1]);
title('CDF');
function probdf = mybernoli(k,n,p)
m =5000 ;
idxx = 0;
for i=1:m
idxx= idxx+ double(nnz(rand(n,1) < p)==k);
end
probdf = idxx/m;
end
k = 0:5000;
y1_pdf = mybernoli(k,20,0.5);
y1_cdf = cumsum(y1_pdf);
figure;
subplot(1,2,1);
stem(k,y1_pdf);
title('PDF');
subplot(1,2,2);
stairs(k,y1_cdf);
axis([0 20 0 1]);
title('CDF')
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