shot Ink 0.25 mm 0.35 mm 0.5 mm 0.7 mm 1 mm 203 PM Colour Problem 6 [23 points]: Suppose we flip a coin 87 times. Assume that the coin is fair. a) [2 points] Compute the probability of obtaining 53 heads. shot 102 PM b) [3 points] Verify if the Rule of Five is satisfied? Compute the probability of obtaining 53 heads based on Normal approximation. Is the answer close to part a)? c) [3 points] Compute the probability of obtaining at least 53 heads based on the Normal approximation. d) [3 points] Find the number of heads which have the largest probability based on the Normal approximation Suppose the coin is biased (loaded) with p = Pr(Head) = 0.02 lamas e) [2 points] What is the exact probability of obtaining at most one head? f) [3 points] Which approximation can we use this time? Poisson approximation or Normal approximation? Why? g) [3 points] Estimate the probability in part (e) based on Poisson approximation. h) [4 points] Estimate the probability in part (e) based on Normal approximation and PM verify which one is more accurate