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Problem:
A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double or nothing. Based on past performance, the likelihood of doubling one's money is 0.6, while the chance of losing an investment is 0.4. Money earned one year can be reinvested in a later year and investments are restricted to unit amounts.
When dynamic programming is used to find the investment strategy for the next 4 years that will maximize the expected total holdings at the end of that period, the problem is formulated as a four-stage process with each stage representing a year. The states sj are the amounts of money available for investment for stage j (j = 1; 2; 3; 4).
Let fj(sj) denote the maximum expected holdings at the end of the process, starting in state sj at stage j.
(a) By clearly explaining your reasoning show that a recursive formula for finding the maximum expected holdings at the end of four years is given by
for j = 1; 2; 3 and 4, where the values of α and β are to be determined.
(b) Write down an expression for f5(s).
(c) Find the maximum expected holdings at the end of the four years.
Bob is 2 years from being double as old as Ellen. The sum of twice Bob's age and three times Ellen's age is 66. How old is Ellen? Let x = Ellen's age and let y = Bob's age. Sin
Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil
A patient will receive hemodialysis for 2.5 hours. The amount of fluid removed per hour is 1.4 liters. The total amount removed in liters, will be
LARGE SAMPLES These are samples that have a sample size greater than 30(that is n>30) (a) Estimation of population mean Here we suppose that if we take a large sample
S olve the subsequent IVP. dv/dt = 9.8 - 0.196v; v(0) = 48 Solution To determine the solution to an Initial Value Problem we should first determine the gen
Euler''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
what is slope
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
The time has at last come to describe "nice enough". We've been using this term during the last few sections to explain those solutions which could be used to form a general soluti
Evaluate the log function: Calculate 3log 10 2. Solution: Rule 3. log (A n ) = nlog b A 3log 10 2 = log 10 (2 3 ) = log 10 8 = 0.903
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