You are a financial analyst and your boss is ready to give you a bit more responsibility and allow you to interact directly with clients. You are tasked with picking a stock to pitch to your first client. You want to present a robust analysis of the stock of your choice. Using the past 3 years of data, please write an R-script that answers the following questions:

1. Analyze the daily distribution of returns plot the density function. Does it look like its normally distributed?
2. Estimate the annual mean returns and annual standard deviation of returns.
3. Simulate the daily price path over the next 6 months (approximately 126 days) using the estimates from (2) above and assuming that prices follow a lognormal distribution. Plot the outcome of the simulation.
4. Simulate ten expected daily price paths like the one in (3) above and graph them on the same graph.
5. Your client wants to invest a large amount into the stock you picked, but they have a fairly short horizon of only 35 days. You oversee risk management for your client and decided to run a VaR analysis for the given horizon. What is the worst-case scenario for the stock price 35 days from now (with 99% certainty)?