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# A sum of \$50,000 is invested at a rate R, selected from a ISBN: 9780321923271 41

## Solution for problem 7E Chapter 5.1

Probability and Statistical Inference | 9th Edition

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Problem 7E

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 eR dollars is the amount at the end of that year.

(a) Find the cdf and pdf of X.

(b) Verify that X = 50000 eR is defined correctly if the compounding is done instantaneously. Hint: Divide the year into n equal parts, calculate the value of the amount at the end of each part, and then take the limit as n→∞.

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Physics Electricity and Magnetism (Professor Perdekamp) : ​Week 1 Notes ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ Prelecture: Coulomb’s Law ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­...

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##### ISBN: 9780321923271

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