This problem is another entry in our \"numerical approximation of x\" series. As

Question

This problem is another entry in our "numerical approximation of x" 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 z-y plane, the random point P(x_0, y_0) is confined to a 1-by-1 square cornered on the origin (OABC in Figure 1). Recall that r_0 root x^2_0 + y^2 _0 gives the distance between P and the origin O. 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 1000 counts and creating two real random numbers between 0 and 1 for x_0 and y_0 (b) 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 (5 points for each part)

Explanation / Answer

countC = 0
totalCount = 10000
for i = 1:totalCount
x = rand()
y = rand()
r = sqrt(x*x + y*y)
if r <= 1
countC = countC + 1
end
end

calc_pie1 = 4*(countC/totalCount)

calc_pie2 = 0
total_count = 0
count_c = 0
err = 0.000000009

while(abs(pi - calc_pie2) > err)
total_count = total_count + 1
x = rand()
y = rand()
r = sqrt(x*x + y*y)
if r <= 1
count_c = count_c + 1
end
calc_pie2 = 4*(count_c/total_count)
end

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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