1. Let's assign numerical values to coin flips: Heads is +1 and Tails is –1, each with probability ½. After a huge number of coin flips, you'd expect an average value of µ = 0, because you'd expect roughly as many Heads (+1) as Tails (-1), so on average they would cancel out to 0. Since Heads and Tails are both 1 unit of deviation away from the mean, the standard deviation is just o = 1. Suppose that you flip a coin n = 100 times. a) If you get 49 Heads and 51 Tails, what is the “mean coin flip score" x? Hint: just apply the usual definition of mean: add up all the values, with +1 for each Head and -1 for each Tail, then divide by 100. b) Spoiler alert: the answer to part (a) is = -0.02. Use this to answer the following: what is the probability that, if you flip a coin 100 times, you get 49 Heads or fewer? Hint: calculate the z-score for this sample, using z = (x - µ) / (0/Vn), and then use the chart. c) Now repeat the procedure to figure out the probability that, if you flip a coin 100 times, you get 45 Heads or fewer. d) Finally, what are the odds of getting just 40 Heads or fewer out of 100 coin flips?

1. Let's assign numerical values to coin flips: Heads is +1 and Tails is –1, each with probability ½. After a huge number of coin flips, you'd expect an average value of µ = 0, because you'd expect roughly as many Heads (+1) as Tails (-1), so on average they would cancel out to 0. Since Heads and Tails are both 1 unit of deviation away from the mean, the standard deviation is just o = 1. Suppose that you flip a coin n = 100 times. a) If you get 49 Heads and 51 Tails, what is the “mean coin flip score" x? Hint: just apply the usual definition of mean: add up all the values, with +1 for each Head and -1 for each Tail, then divide by 100. b) Spoiler alert: the answer to part (a) is = -0.02. Use this to answer the following: what is the probability that, if you flip a coin 100 times, you get 49 Heads or fewer? Hint: calculate the z-score for this sample, using z = (x - µ) / (0/Vn), and then use the chart. c) Now repeat the procedure to figure out the probability that, if you flip a coin 100 times, you get 45 Heads or fewer. d) Finally, what are the odds of getting just 40 Heads or fewer out of 100 coin flips?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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