Table of Distributions.docx - TYPE OF DISTRIBUTION NORMAL...

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TYPE OF DISTRIBUTION PROBABILITY DENSITY FUNCTION (p.d.f) [ f(x) ] MOMENT GENERATING FUNCTION (m.g.f) [ M X (t) ] [ E(e tx ) ] MEAN [ E(X) ] VARIANCE [ Var (X) ] NORMAL DISTRIBUTION X~N(µ,? 2 ) f ( x ) = 1 σ 2 π e −( x μ ) 2 2 σ 2 e μt + σ 2 t 2 2 µ ? 2 UNIFORM DISTRIBUTION X~U(A,B) f ( x ; A ,B ) = { 1 B A , A≤ x≤B 0 ,elsewhere e tA e tB t ( B A ) A + B 2 B A ¿ 2 ¿ ¿ ¿ GAMMA DISTRIBUTION X~Gamma (α,β) f ( x ;α , β ) = { 1 β α Γ ( α ) x α 1 e x β ,x ≥ 0 0 ,elsewhere
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