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3. You did (or will do} this problem in section on 1036 : FPP.16.A.4 and will now use R to solve it. Here is the problem again: {a} A coin is toued, and you win a dollar if there are more than 60% heads. Which is better: 10 tosses or 100? Explain. {b} As in {a}, but you win the dollar if there are more than 40% heads. {c} As in {a}, but you win the dollar if there are between 40% and 60% heads. ['d} As in {a}, but you win the dollar if there are exactly 50% heads: Now, using R to do this problem: {a} First create a vector called coin: Then sample from this 10 times with replacement (simulating toning the coin} and count how many heads you got. Did you get more than 6 heads? You can check this using sum (and) where \":96" returns TRUE or FALSE: Repeat this (sampling 10 times and counting the number of heads, and seeing if the number of heads in 10 tosses was more than 6} 1000 times and collect the sum of heads in a vector called toasesl. Count how many times the sum of heads was more than 6: Compute the fraction of times it was more than 6. ['b} Now repeat this entire procedure with 100 tosses. Call the resultant vector toasesi. Again, compute the fraction of times that the number of heads was over 60%. How will you use this to answer problem lfa} above? {c} Repeat the procedure as in {a} but now you are looking to estimate the chance that the fraction of heads is more than 40%. {d} Repeat the procedure as in {a} but now you are looking to estimate the chance that the fraction of heads is more than 40% but not more than 60%