Vgamestock.csv" contains daily prices and returns of three stocks: ATVI, EA, and TTWO. Use only the variable denoted by "TTWORet" (contains daily returns for TTWO for 252 days) to answer the questions below.

Assume that we are interested in the number of days that the TTWO stock was up (relative to the previous day) over 5 trading days (note that we can assume that a stock going down would potentially include staying the same). Let us denote this variable by X.

a) What is the probability that the TTWO stock will be up 2 days or less in the next 5 days? b) Compute the probability that the TTWO stock (over 5 trading days) will be up within one standard deviation of its mean, (()()+)=?

c) Plot the estimated probability distribution against the empirical distribution (actual data) for the number of days that the TTWO stock was up (relative to the previous day) over 5 trading days. Do you think the model provides a reasonable fit to data?

"Vgamestock.csv" file link: https://drive.google.com/file/d/1-GB59h002_QUfBEIpFw_d0JnmSG5HXyI/view?usp=sharing