Publications by Sang Lee 116990394
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In this project we will explore empirical probability using random samples. The two important functions to understand are “sample” and “replicate”. We use the sample function to set up our experiment, and replicate function to repeat it as many times as we want. 1 Rolling Die 1.1 Fair Die Setup the experiment where we roll two fair six ...
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An interesting application of conditional probability is the Monty-Hall problem, whose solution intrigued many, including career mathematicians (life is hard!). There is a lot of trivia around this problem in the internet, a good place to start would be the Wikipedia article here: https://en.wikipedia.org/wiki/Monty_Hall_problem In this project w...
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1 Normal Distibution In this section we will explore the normal distribution. 1.1 Fixed mean, varying standard deviation Set \(\mu = 5\). For values of \(\sigma\) given by \(0.2, 0.4, 0.8, 1, 1.3, 1.8, 2\), plot the densities of \(N(\mu, \sigma)\) in the same plot. It might help if (1) you have the densities of \(N(\mu = 5, \sigma = 0.2)\) and \...
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1 Visualizing Discrete Distributions In this problem we will draw plots for some of the discrete probability distributions that we have studied in class 1.1 Binomial distribution. We will plot the density function for the binomial distribution Bin(n, p). Note: 1) The values for this random variable are 0, 1, 2, …, n. 2) The density plot will h...
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1 Visualizing Discrete Distributions In this problem we will draw plots for some of the discrete probability distributions that we have studied in class 1.1 Binomial distribution. We will plot the density function for the binomial distribution Bin(n, p). Note: 1) The values for this random variable are 0, 1, 2, …, n. 2) The density plot will h...
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Recall the hit-and-run example from lecture and HW4. We noted that the Bayes’ probabilities are calculated as the following formula \[ P(B|W) = \frac{pq}{pq + (1-p)(1-q)},\] where \(P(B) = q\) and \(P(W|B) = p\) (check notes). We also noted in HW4 that if \(P(W|B)=p > \frac{1}{2}\) we will have \[ P(B|W) > P(B).\] In this problem, we will explo...
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