Blog Archives

Normal, Chi-Squared and Gamma Distributions

Here we show the classical example on how the normal, chi-squared, and gamma distributions are related. If \(Z_1, \ldots, Z_n\) are i.i.d. variables with the standard normal distribution, then \(\sum_{i=1}^n Z_i \sim \chi^2_n\). Let \(X_1, \ldots, X_n \sim \text{Normal}(\mu, \sigma^2)\)

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Posted in Probability

Conditional and Marginal Independence

Let \(A, B, C\) be three random variables. Consider the following dependency structures modeled with Bayesian networks. \(A \leftarrow B \rightarrow C\) \(A \rightarrow B \rightarrow C\) \(A \rightarrow B \leftarrow C\) The first two cases both say that \(A\)

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Posted in Probability