Discrete Random Variable: outcomes are limited to a countable/listable set of real numbers (can think of the ‘next’ possible value)

• often the result of counting

Continous Random Variable: outcomes that can be any real number within a certain interval (cannot think of the ‘next’ possible value)

• often the result of measuring (height, distance, weight, etc.)
• there may be ‘discrete values’, however, fractions will still exist
• you’ll tend to ask questions based on a range, rather than a specific value
  • pizza arriving in 10-20 mins, rather than at 10.342 mins
• no point/mass probabilities: $P(X = x) = 0$

Cumultative Distribution Function (CDF):

• works for both discrete & continuous r.v.s.

$F(x) = P(X ≤ x) = \int^{x}_{-\infty}f(x)dx$

Probability Density Function (PDF):

• $f_x(x)$ gives the density of probabilities for a continuous random variable $X$, where

$f_X(x) = \frac{d}{dx}F_X(x)$

Common continuous probability distributions:

Uniform: all values equally likely over some range

Normal: symmetric bell-shaped curve

Exponential: decreasing at exponential rate

Beta: values between 0 and 1