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A sum of $50,000 is invested at a rate R, selected from a
Chapter 5, Problem 7E(choose chapter or problem)
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→∞.
Questions & Answers
QUESTION:
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→∞.
ANSWER:
Step 1 of 6
(a)
From the question its given that:
The probability density function of a uniform distribution is the reciprocal of the difference of the boundaries, on the interval between the boundaries ( 0 elsewhere):
First, we determine 
