Practice matlab and basic simulation techniques

Question

Aim: To practice MATLAB and basic Simulation Techniques 

Question) A gambler makes a series of plays with outcomes X1,X2.......  where the X_i, i>=1 are independent, identically distributed random variables. The cost of each play is c. The gambler can stop at any time n>=1 with the fortune:

The gambler will stop if X_n > β. The gambler wants to maximize the mean of his fortune. What are the best values of β in the following two cases?

1) Case A: c = 0.2 and the distribution of X_n is the exponential distribution, i.e., its density function is

2) Case B: c = 0.1 and X_n is a discrete random variable obeying Poisson distribution:

     P(x=k) = 1/ek! for k= 0,1,2,3....,

Your Task:

i) Find the best of values of β by using Monte Carlo simulation.

ii) Write a report with the following sections:

• Problem: You should explain this problem in a way such that a 16-year old high student student can understand it.

• Method: You should describe and explain your method (not your matlab code) in details.

• Code: your well-structured and well-documented code.

• Experimental Results and Discussion: You report your ex-perimental results here and give some discussions. You should use figures to show your results.

• Conclusion: Summarize what you have done and your reection. Your report should be at most five pages.

Submissions:

1) On-line submission

2) Your submission should include:

a) your report (named by REPORTyourloginname.XXX) and

b) your code file (named by CODEyourloginname.XXX).