Question

Write python or java or c programs to simulate the problems and display the output in a graphical form, with the following simplifications:

5) The triangle has one corner at the origin, one at (1,0), and one at (x,1), repeating the program for x = 0, 1/2, 1.

Problem 5. Consider a triangle and a point chosen within the triangle according to the uniform probability law. Let X be the distance from the point to the base of the triangle. Given the height of the triangle, find the CDF and the PDF of X.

Answer 1

5) The triangle has one corner at the origin, one at (1,0), and one at (x,1), repeating the program for x = 0, 1/2, 1.

ans:-

In python we can plot all three triangle with following code:

import matplotlib.pyplot as plt

plt.plot([0,1,0,0], [0,0,1,0])

plt.plot([0,1,0.5,0],[0,0,1,0])

plt.plot([0,1,1,0],[0,0,1,0])

plt.show()

5. Consider a triangle and a point chosen within the triangle according to the uniform probability law. Let X be the distance from the point to the base of the triangle. Given the height of the triangle, find the CDF and the PDF of X.

ans:-

we have to find the CDF and PDF of t. Consider a triangle and a point chosen with in the triangle. according to the uniform Probability law. Let x'be the distance from the point to the base of triangle. Let 'n be the dista) height of triangle let base of triangle be b. Then area of triangle is: choosen point draw from a randomly a line parallel to the base and let the area of triangle so formed Ax The height of this triangle Ch-x) is and its base length is b(h). so, An - Ch-x) 6 Ch-x) Ax - bahasa we have Fx (x) = 1-P (**) fx (x ): 1-

f (x) = 1 (n- for XE [o, n] for 24 [o,h] i fu (x) 20 So fx (x)= {1 - Chypre xe [o h] o u¢ [o, h] Thus the CDF of x is : P(x2x) = +-P(x>x) -to-Ch-x32m2 , 0<x<by 10) nso ash The PDF is obtained by differenting COF: fu)- I a [P(X<x)} - 82(h-x)/m2, ourch otherwise

If u have any doubt please ask me.