Continuous Random Variables and Probability Density Functions

An alternative way of approximating a binomial distribution is considered that leads to a continuous random variable (one that takes on an infinite number of values), known as the normal or Gaussian. Continuous random variables have probability density functions, rather than probability distributions, associated with them, and this leads to probabilities having to be calculated as an area under the function, which requires integral calculus. The standard normal distribution is introduced as a convenient way of calculating normal probabilities and examples of how to do such calculations are provided. Distributions related to the normal — the chi-square, Student’s t and the F — along with the concepts of independence and covariance between random variables are introduced. Methods of simulating random variables and distributions are discussed . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.