Chapter 8: Miscellaneous Methods

1. State the three main types of transformations of a random variable / vector.
2. State the three main methods for determining the distribution of a transformed random variable / vector.
3. Use the cumulative distribution method to determine the cumulative distribution \(F_{Y}\) of a transformed random variable \(Y = g(X)\) using the cumulative distribution function of \(X\).
4. Define the order statistics of a sample.
5. Determine the distribution of the maximum of a random sample, given the cumulative distribution function for the random sample.
6. Determine the distribution of the minimum of a random sample, given the cumulative distribution function for the random sample.
7. Determine the cumulative distribution function of the sum of two random variables.
8. Use the convolution integral to determine the probability density function for the sum of two independent random variables.