Problem 1. Suppose you toss an unbiased coin (i.e. $p=.5$) 50 times. Consider $X$, the total number of heads that you obtain. (a) What's the average of $X$? Remember that this is also called the mean. (b) What's the variance? (c) Using the answers for (a) and (b), write down the corresponding Gaussian distribution that approximately fits $P(X)$. (d) Calculate $P(51)$ and $P(-1)$ using this Gaussian approximation. (e) What should the exact answer be?