Definition: Let \(X_{1}, X_{2}, \ldots, X_{n}\) be random variables and let \(c_{1}, c_{2}, \ldots, c_{n}\) be constants. Then, $$ \text{Y}=\text{c}_{1} \text{X}_{1}+\text{c}_{2} \text{X}_{2}+\cdots+\text{c}_{\text{n}} \text{X}_{\text{n}} $$ is a linear combination of \(X_{1}, X_{2}, \ldots, X_{n}\). In this reading, however, we will only…

Let \(\text{X}\) and \(\text{Y}\) be two discrete random variables, with a joint probability mass function, \(\text{f}(\text{x}, \text{y})\). Then, the random variables \(\text{X}\) and \(\text{Y}\) are said to be independent if and only if, $$ \text{f}(\text{x}, \text{y})=\text{f}(\text{x}) * \text{f}(\text{y}), \quad \text…