Math Problem Statement

Compute mean and variance of the following well-known distributions: (i) Binomial (n, p), (ii) Poisson (µ), (iii) Normal (m, σ), (iv)Gamma (l) and (v) Cauchy (λ, µ).

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Distributions
Mean
Variance

Formulas

Mean of Binomial: μ = n * p
Variance of Binomial: σ^2 = n * p * (1 - p)
Mean of Poisson: μ = μ
Variance of Poisson: σ^2 = μ
Mean of Normal: μ = m
Variance of Normal: σ^2 = σ^2
Mean of Gamma: μ = k / λ
Variance of Gamma: σ^2 = k / λ^2
Mean of Cauchy: Undefined
Variance of Cauchy: Undefined

Theorems

Law of Large Numbers
Central Limit Theorem

Suitable Grade Level

Undergraduate