a.) (13 points) Suppose that the coordinates of a point (X, Y ) are such that X
ID: 3044116 • Letter: A
Question
a.) (13 points) Suppose that the coordinates of a point (X, Y ) are such that X U[0, 1) and Y U[0, 1). Compute the probability that the distance from this point to the origin is less than or equal to L. You should consider the two cases when
0 L 1 and when 1 L 2.
and you should check your results using a Monte-Carlo simulation of 3000 trials for various values of L.
b.) (7 points) Compute the average distance a point will be from the origin and you should check your results using a Monte-Carlo simulation of 3000 trials.
Explanation / Answer
Point X,Y lies in a square with end points (x,y) as (0,0), (1,1) , (0,1) , ( 1,0)
Probability that distance from this point to the origin is less than or equal to L = L^2/2
b) Average distanc =1/sqrt(2)
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