Continuous Random Variable

A continuous random variable X can assume any real value within a specified interval. Probabilities are described by a p

Random Variables

Cumulative Distribution Function

The cumulative distribution function F(x) = P(X ≤ x) gives the total probability for all values up to and including x. F

Random Variables

Discrete Random Variable

A discrete random variable X assigns numerical values to outcomes of a random experiment and can only take on specific,

Random Variables

Probability Density Function

A probability density function f(x) for a continuous random variable X satisfies f(x) ≥ 0 for all x, and ∫f(x)dx = 1 ove

Random Variables

4.1: Random Variable

A function that assigns numerical values to the outcomes of a random experiment. Discrete random variables take specific

Random Variables

4.1: Random Variable

For a discrete random variable, a table or formula showing P(X = x) for each possible value x. For a continuous random v

Random Variables

4.2: Expected Value

The mean or average value of a random variable, calculated as E(X) = ΣxP(X = x) for discrete variables or E(X) = ∫xf(x)d

Random Variables

4.2: Expected Value

Variance measures the spread of a random variable about its mean, calculated as Var(X) = E[(X - μ)²] = E(X²) - [E(X)]²,

Random Variables