MATLAB This problem is another entry in our\" numerical approximation of pi\" se

Question

MATLAB

This problem is another entry in our" numerical approximation of pi" series. Assume that you have created x_0, and y_0; two real random numbers between 0 and 1. If x_0 and y_0 are coordinates of a single point P in the x - y plane, the random point P (x_0, y_0) is confined to a 1-by-l square cornered on the origin (OABC in Figure 1). Recall that r_0 = Squareroot x^2_0 + y^2_0 gives the distance between P and the origin O. We know that the probability of r_0 being less than 1 (i.e. the probability for point P to be confined to circular sector OAC) is equal to the area of the circular sector OAC over the area of the square OABC or pi/4. Write a program to calculate the value of pi from this method by using a for loop for 1000 counts and creating two real random numbers between 0 and 1 for x_0 and y_0. Repeat the problem once more except this time by using a while loop, find out how many times you need to repeat the loop to calculate pi with 10^-9 difference from the exact value defined by MATLAB variable pi. This problem is worth 10 points

Explanation / Answer

a.

count = 0;       %%count counts number of time the value of r is less than 1
for i = 1 : 1000
    x = rand;
    y = rand;
    r = sqrt(x^2 + y^2);
    if r <= 1
        count = count + 1;
    end
end
prob = count / 1000; %%we divide count by 1000 since we already know that loop itterated 1000 times
p = prob * 4;            %% we know that prob = pi/4
fprintf ("our estimated pi value is %d ",p);

___________________________________________________________________________

b.

count_less = double(0);            %%count_less counts number of time the value of r is less than 1
count_experiment = double(0);%%count_experiment counts number of time experiment is carried out
prob = double(0);
while abs(pi - prob*4) > 10^-9   %%prob is pi/4, so we multiply prob with 4 and then compare
    x = rand;
    y = rand;
    r = sqrt(x^2 + y^2);
    count_experiment = count_experiment + 1;
    if r <= 1
        count_less = count_less + 1;
    end
    prob = count_less/count_experiment; %probability need to be calculated in every itteration
end;
fprintf ("Itteration required = %d ",count_experiment);

____________________________________________________________________________

Hope that the above code-segment helps you. The code is self-explanatory and very simple

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.