The daily demand for newspapers can be approximated very well with a random variable Gamma(a, 3) with an expected value of 10,000 and a variance of 1,000,000. The printing press can produce 11,000 copies per day. The profit per newspaper sold is $10, and the cost of each newspaper not sold is $2.50 1. Calculate the expected value of profit using the Monte Carlo method in r code and estimate its standard error using 10,000 simulations 2. Consider that a Y Gamma(m, 3) can be decomposed as Y=BX were X, Exp(1), use the method of antithetical variables to construct an estimate of the expected profit using 10,000 simulations of newspaper sales 3. What was the relative gain in standard error using the method of opposite variables in r ? How narrow are the confidence intervals?