Continuous DistributionsMean
Variance
MomentGenerating
Function
1
; θ ≤ y ≤ θ2
θ2 − θ1 1
θ1 + θ2
2
(θ2 − θ1 )2
12
etθ2 − etθ1
t (θ2 − θ1 )
1
1
2
(y
−
µ)
√ exp −
2σ 2
σ 2π
−∞ < y < +∞
µ
σ2
β
β2
(1 − βt)−1
αβ
αβ 2
(1 − βt)−α
v
2v
(1−2t)−v/2
α
α+β
(α + β) (α + β + 1)
Distribution
Uniform
Normal
Exponential
Probability Function
f (y) =
f (y) =
f (y) =
Gamma
Chi-square
f (y) =
1
α−1 −y/β
e
;
α y
(α)β
0
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