Continuous Distributions Distribution Uniform Normal Exponential Gamma Chi-square Beta Probability Function f (y) = f (y) = 1 ; θ ≤ y ≤ θ2 θ2 − θ1 1 1 1 (y − µ)2 √ exp − 2 2σ σ 2π −∞ < y < +∞ f (y) = 1 y α−1 e−y/β ; (α)β α 0<y<∞ f (y) = f (y) = f (y) = 1 −y/β e ; β>0 β 0<y<∞ (y)(v/2)−1 e−y/2 2v/2 (v/2) y2 > 0 ; (α + β) y α−1 (1 − y)β−1 ; (α) (β) 0<y<1 MomentGenerating Function Mean Variance θ1 + θ2 2 (θ2 − θ1 )2 12 µ σ2 β β2 (1 − βt)−1 αβ αβ 2 (1 − βt)−α v 2v
Premium Normal distribution Probability theory
College Physics OpenStax College Rice University 6100 Main Street MS-380 Houston‚ Texas 77005 To learn more about OpenStax College‚ visit http://openstaxcollege.org. Individual print copies and bulk orders can be purchased through our website. © 2013 by Rice University. The textbook content was produced by OpenStax College and is licensed under a Creative Commons Attribution 3.0 Unported License. Under the license‚ any user of the textbook or the textbook content herein must provide proper attribution
Premium Magnetic field Classical mechanics Quantum mechanics