Continuous Random Variables

Abstract

This chapter introduces some properties of continuous random variables. If a random variable follows a uniform probability distribution in some interval, then any subinterval of possible values of equal length will be equally likely. The most important probability distribution of all is the normal distribution, which is applied very often in practice and has a number of properties that are useful for inference. For any normal random variable, we can calculate probabilities through transforming it into a standardized normal random variable. The normal approximation will be good as long as the binomial distribution is not too skewed to the left or the right. A preferred way to check this is by evaluating the expected successes and expected failures. The chapter discusses continuous random variables having asymmetric distributions such as exponential distribution. It features practice problems designed to ensure that readers understand the concepts and can apply them using real data.