Definitions [2]
Definition: Probability Distribution of Discrete Random Variables
If a random variable X takes values x₁, x₂, …, xₙ with respective probabilities p₁, p₂, …, pₙ, then it is called the probability distribution of X.
Definition: Expected Value
If a discrete random variable X has possible values x₁, x₂, …, xₙ with corresponding probabilities p₁, p₂, …, pₙ, then the expected value E(X) is defined as
E(X) = x₁p₁ + x₂p₂ + … + xₙpₙ = Σ xᵢpᵢ
E(X) is also called the mean, which is denoted by μ.
Formulae [3]
Formula: Expected Value
E(X) = Σxᵢpᵢ
Formula: Variance
Var = E(X²) − [E(X)]²
Formula: Standard Deviation
\[\mathrm{SD}(X)=\sqrt{E(X^{2})-\left[E(X)\right]^{2}}\]
SD = √Var
