Hello - please provide step by step calculations and steps taken so that I can check work. Many thanks!

Problem 1. [10 points] Expected value, Variance, Covariance. Stock A is sold for $1. Each day, it increases by 80% (to a value of $1.8) with probability 0.5, or decreases by 20% (to a value of $0.8) with probability 0.5. The movement each day is independent of other days. a. [2 points] If you buy stock A today for $1, what is its expected value tomorrow? Answer: b. [2 points] If you buy stock A today, what is the standard deviation of its value tomorrow? Answer: c. [2 points] If you buy stock A today, what is its expected value and standard deviation in two days? Answer:Another stock, stock B, is traded in the market and has the following behavior. If stock A goes up by 80% (which occurs with probability 0.5) then stock B goes down by 80%, and if stock A goes down by 20% (which occurs with probability 0.5), then stock B goes up by 20%. d. [2 points] If you take $1 and split it equally into the two stocks (i.e., 50 cents in each), what is the expected value of the portfolio value in $'s after one day? Answer: e. [2 point] What is the correlation coefficient between stocks A and BY Note: no need for a rigorous derivation and calculations just state the answer and explain your reasoning...