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Solutions to Problem Set 2

# Note that it is fine for a probability distribution

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Unformatted text preview: erval. This approach makes it is easier to compare the empirical and the normal distribution graphs. The approach that the majority of students have followed was to plot the pdf of the normal distribution and compare it to the empirical distribution. This is also ok. However, you run into the fact that a probability distribution function may be greater than 1 but the empirical frequency cannot. This is the case when the variance is small, which is true for daily returns like we are considering here. Note that it is fine for a probability distribution function to exceed 1. The pdf is only telling you that the probability of an infinitesimal interval of size ε around x is ε×f(x). Even if f(x) is greater than 1, the total probability will be not exceed 1 because ε is very small. c) Compare the empirical histogram with the normal distribution. The empirical histogram and the probabilities obtained from the normal distribution are depicted...
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