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Sample points randomly from a unit sphere. How do you get uniform variables? sample random standard normal variables X1, X2, X3 for the 3 coordinates of the point in the sphere. Then (X1,X2,X3)/sqrt(X1+X2+X3) = (X1,X2,X3) is uniform. What is the variance of each of these uniform variables?
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Quant Research Intern

Interviewed at Citadel

4★
Feb 26, 2021

Sample points randomly from a unit sphere. How do you get uniform variables? sample random standard normal variables X1, X2, X3 for the 3 coordinates of the point in the sphere. Then (X1,X2,X3)/sqrt(X1+X2+X3) = (X1,X2,X3) is uniform. What is the variance of each of these uniform variables?

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