Use R Studio code to answer the questions please provide the code for the answer to the following questions.

1.There is 40% chance that the value of an companys stock goes up by 75 USD and 40% chance that it will not change and 20% chance that it will go down by 30 USD. Plot the probability distribution of average return on this stock for 80 trading days. What is the value of your expected return assuming that the number of trading days is sufficiently large? In plain English, explain what it means to have this value of expected return.

2.What is the variance in your return? Plot the variance as a function of the number of trading days (Hint: I am asking about the variance in return not the variance in average return. Be careful when you are changing the code).

3.Repeat the analysis in question 1 for 800 trading days instead of 80. How does the expected value (mean) and variance (of the return not the average return) change?

4.Suppose the probabilities of going up, remaining constant and going down are (40%, 30%, 30%), how do the expected value and variance change for 120 trading days? How do they change for 1200 trading days?