Probability Distributions

A random variable is a real

A random variable is a real-valued function that assigns a unique real number to every outcome of a random experiment. It is formally defined as X: S

A discrete random variable can take

A discrete random variable can take only finite or countably infinite distinct values. Examples include the number of defective items in a batch, numb

A continuous random variable can take

A continuous random variable can take any value within an interval of real numbers (uncountably infinite values). Examples include height, weight, tim

For a discrete random variable X

For a discrete random variable X, the PMF is denoted as f(x) = P(X = x) and gives the probability that X takes the value x. Properties: f(x) ≥ 0 for a

For a continuous random variable X

For a continuous random variable X, the PDF f(x) is a non-negative function such that: f(x) ≥ 0 for all x in the support, ∫ f(x)dx = 1 over the entire