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Exercise III.4. Suppose that for i i is a random variable R; which is uniformly distribution on [0.01, 0.03], and that R1, R2, ... are independent. A capital of 1 unit grows to II-, (1 + Ri) units in months 1, . . . , n. 1, 2,..., the interest rate obtained in month ..)

Exercise III.4. Suppose that for i i is a random variable R; which is uniformly distribution on [0.01, 0.03], and that R1, R2, ... are independent. A capital of 1 unit grows to II-, (1 + Ri) units in months 1, . . . , n. 1, 2,..., the interest rate obtained in month ..)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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Exercise III.4. Suppose that for i = i is a random variable R; which is uniformly distribution on [0.01,0.03], and that R1, R2, ... are independent. A capital of 1 unit grows to [I-1(1 + R;) units in months 1, . . . , n. 1,2, ..., the interest rate obtained in month
Transcribed Image Text:Exercise III.4. Suppose that for i = i is a random variable R; which is uniformly distribution on [0.01,0.03], and that R1, R2, ... are independent. A capital of 1 unit grows to [I-1(1 + R;) units in months 1, . . . , n. 1,2, ..., the interest rate obtained in month
a. Compute the expected capital after 12 months in an account that starts with 1 unit. b. Compute the variance of the capital after 12 months in an account that starts with 1 unit. Now suppose that a random client invests 10 units and leaves the money in the ac- count for N ~ Poisson(12) months, where N, R1, R2, ... are independent random variables. c. Compute the expected capital at the time of withdrawl of this client.
Transcribed Image Text:a. Compute the expected capital after 12 months in an account that starts with 1 unit. b. Compute the variance of the capital after 12 months in an account that starts with 1 unit. Now suppose that a random client invests 10 units and leaves the money in the ac- count for N ~ Poisson(12) months, where N, R1, R2, ... are independent random variables. c. Compute the expected capital at the time of withdrawl of this client.
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