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Distribution of Functions with Random Variables

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A sum of $50,000 is invested at a rate R, selected from a uniform distribution on the interval (0.03, 0.07). Once R is selected, the sum is compounded instantaneously for a year so that X= 50000 e^R dollars is the amount at the end of that year.

a) Find the distribution function and the p.d.f. of X.

b) Verify that X = 50000e^R is defined correctly if the compounding is done instantaneously.

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