6 Probability Distributions

There is a YouTube video and slides associated with this chapter:

• Probability Distributions - Video
• Probability Distributions - Slides

In order to associated more complex probabilities to a sample space, we need to employ probability distributions. In a first part, the concept of random variables is presented including expected value and variance of a random variable. The two remaining parts of this chapter cover probability distributions for discrete and continuous random variables, respectively. For each probability distribution, the respective names and commands in R are presented. Many probability distributions in R have a “name” (presented in parenthesis in the lists below). The following discrete probability distributions are presented:

• Bernoulli Distribution
• Binomial Distribution (“binom”)
• Poisson Distribution (“pois”)

Continuous distributions included in this chapter are:

• Uniform Distribution (“unif”)
• Normal Distribution (“norm”)
• Student Distribution or t-Distribution (“t”)

There is a particular set of R commands to find various aspects of the distributions:

• dname() for the density or probability function
• pname() for the cumulative density function
• rname() for the random numbers
• qname() for the inverse