The Rate of Return for a Stock - Statistics Assignment Help

Assignment Task:

Task:

1) (6 pts) Use the fitdistrplus library to answer the following questions
a) (4.5 pts) The rate of return for a stock each month are uniformly distributed with a minimum of -10% and a maximum of 10%. Demonstrate using goodness of fit statistics that the returns after 5 years will follow a lognormal distribution. What are the paremeters of the underlying normal distribution? (Use 10,000 trials)
b) (1.5 pts) A clothing store notices that once a customer enters the store, the time until the next customer will enter the store can be modeled with an exponential function, with a mean of 10 minutes. Show using graphical methods that the number of customers that enter the store in an hour will follow a Poisson distribution. What are the parameters of the distribution? (Use 100,000 trials)

2) (6 pts) A man decides to begin operating a coffee truck. His only offerings are hot coffee and iced coffee. Every morning, he brews enough for 70 servings of iced coffee, and brings enough beans and filters to make 70 servings of hot coffee. Any iced coffee that isn’t bought is discarded at the end of the day for no profit. The hot coffee he makes to order, so none is ever wasted.

Demand for iced coffee follows a Poisson distribution with mean 50, and demand for the hot coffee follows a normal distribution with mean 60, and standard deviation 15. The Spearman correlation for demand for both is 0-.6.

The iced coffee sells for $4.50 and costs $1.25 per serving to make. The hot coffee sells for $3.50 and costs $1.25 per serving to make. The food truck costs $150 per day to operate. Simulate the man’s daily profit in R, using 10,000 trials
a) What are the mean and standard deviation of his profit?
b) Provide a 90% confidence interval for his profit on a given day.
c) Provide a 90% confidence interval for his mean profit.
d) How many trials would it to provide a 99% confidence interval with a half-width of $0.50 for his mean profit?
e) What would be the standard deviation of his profit if iced and hot coffee sales were uncorrelated?

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