Strings in Java
Recall that a class is a description of an object type. An object is an instantiation of a class. A class may have one or more constructors, which are called when an object is created. An object variable is essentially …
Static Methods in Java
A static method in a class is a method declared with the static modifier. The following is a class Helper defined with static methods abs() and main(): The signature of the method abs() is: It has the following parts: public: …
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 \(X_1, \ldots, X_n \sim \text{Normal}(\mu, \sigma^2)\) …
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 \(A\) …