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A circle with a random radius R ~ Unif(0, 1) is generated. Let A be its area. (a) Use simulations in R (the statistical programming

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A circle with a random radius R ~ Unif(0, 1) is generated. Let A be its area. (a) Use simulations in R (the statistical programming language) to numerically estimate the mean and the variance of A. (b) Find the theoretical mean and the variance of A, without first finding the CDF or PDF of A. Compare with your numerical results from (a). (b) Find the CDF and PDF of A

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