Distribution of a linear transformation of a discrete random variable
A discrete model assigns an integer payoff to each outcome
Let \(X\) be the discrete random variable with the following distribution
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(2\) | \(\frac{4}{7}\) |
| \(4\) | \(\frac{1}{7}\) |
| \(5\) | \(\frac{2}{7}\) |
Define \(Y\) by the rule
\[Y = 3\,X + 1.\]