Generation of a random sample of a normally distributed, Basic Statistics

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Generation of a random sample of a normally distributed

Generation of a random sample of a normally distributed random variable. Let U₁, U₂ be independent random variables, each uniformly distributed on the interval 0 to 1. Show that the random variables

are independent random variables, each normally distributed with mean 0 and variance 1. (For a discussion of this result, see G. E. P. Box and Mervin E. Muller, "A note on the generation of random normal deviates," Annals of Mathematics Statistics, Vol. 29 (1958), pp. 610-611.)

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