• One of many concepts of statistics
• Probability is defined as the likelihood of a certain event to happen
• Often described as a ratio of two numbers: (Number of times the event occurs):(Number of possible chances the event can occur)
• Probability distributions allow for different types of data to be expressed in multiple ways

Two different types of data are plotted in different ways

Continuous data is not measured and falls in a range: Outdoor temperature, a persons height

• Uses Uniform, Exponential, and Normal plots

Discrete data is measurable data: Classroom gender, number of computers in a computer lab

• Uses Binomial, Geometric, and Hypergeometric plots

highs <- c(80, 79, 78, 71, 71, 75, 76)
ggplot(data = data.frame(highs), aes(x = highs)) +
  geom_density(fill = "skyblue") + labs(title = "High
    Temperatures in Phoenix Last Week", x = "Temperature (F)",
      y = "Density")

A function that represents continuous data is the Probability Density Function (PDF)

• This function represents continuous random variables, bounded by a and b, and is given by the formula:

\[ f(x) = \begin{cases} \frac{1}{b - a} & \text{for } a \leq x \leq b, \\ 0 & \text{for } x < a \text{ or } x > b. \end{cases} \]

where a and b are the lower and upper bounds of the interval

A function that represents discrete data is the Probability Mass Function (PMF)

• This function represents discrete random variables, given by the formula

\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]

where: n is the total number of chances, k is the number of successes, p is the probability of success on each chances

• Key differences include a PDF is strictly for continuous data, and a PMF is strictly for discrete data