Estimating The Value Of The following figure suggests how t

Estimating The Value Of ?. The following figure suggests how to estimate the value of ? with a simulation. In the figure, a circle with area equal to ?/4 is inscribed in a square whose area is equal to 1. One hundred points have been randomly chosen from within the square. The probability that a point is inside the circle is equal to the fraction of the area of the square that is taken up by the circle. That fraction is ?/4. We can therefore estimate the value of ?/4 by counting the number of points inside the circle which is 76, and dividing by the total number of points, which is 100, to obtain the estimate ?/4 = 0.76. From this we conclude that ? ? 4(0.76) = 3.04. This exercise presents a simulation experiment that is designed to estimate the value of ? by generating 1000 points in a circle of radius 1.

1. Generate 1000 values of a Uniform RV distributed from -0.5 to 0.5 and store in Column C1.

2. Generate 1000 values of a Uniform RV distributed from -0.5 to 0.5 and store in Column C2.

3. Compute the square of the distance from each point (Xi, Yi) to the origin and store in Column C3.

JUST need help with number 3

Solution

The MINITAB output of random generation is shown below:

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