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cheat - G(y =-y-1 e-y 1)G-1(y G1(y = 1 e-y R(n P{i = pi = 1...

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R ( n ) : P ( { ω i } ) = p i = 1 n if 0 i n - 1 0 otherwise B ( n, p ) : p k = ( n k ) p k (1 - p ) n - k if 0 k n 0 otherwise max( B ( n, p )) = ( n + 1) p G ( β ) : P ( ω = k ) = p k = (1 - β ) β k , k = 0 , 1 , ... G ( β ) : P ( ω = k ) = p k = (1 - β ) β k - 1 , k = 1 , 2 , ... β = m m + 1 ( m is average waiting time) P ( λ ) : p k = e - λ λ k k ! , k = 0 , 1 , ... Z ( α ) : p k = k - α ζ ( α ) , k = 1 , 2 , ... ; ζ ( α ) = k =1 k - α P Z ( L 1 ) P Z ( L 2 ) = L 1 L 2 α U ( a, b ) : f ( x ) = 1 b - a U ( x - a ) U ( b - x ) for a < b, ( a, b ) Ω R U ( a, b ) : F ( x ) = P ( X x ) = 1 b - a b a I y x ( y ) dy = 0 if x < a x - a b - a if a x b 1 if x b Γ(1) = 1; Γ( x ) = Γ( x - 1)( x - 1) , x Z β ( a, b ) : f ( x ) = Γ( a + b ) Γ( a )Γ( b ) x a - 1 (1 - x ) b - 1 U ( x ) U (1 - x ) , a, b > 0 P ( K = k ) = n k ( a + b - 1)!( k + a - 1)!( n - k + b - 1)! ( a - 1)!( b - 1)!( n + a + b - 1)! ε ( λ ) : f ( x ) = λe - λx U ( X ) , λ = 1 m ε ( λ ) : F ( x ) = P ( X x ) = (1 - e - λx ) U ( X ) Γ( a, λ ) : f ( x ) = λ Γ( α ) ( λx ) α - 1 e - λx U ( x ) , α, λ > 0 F α,λ ( x ) = 1 Γ( α ) G α ( λx ) G α ( y ) = - y α - 1 e - y + ( α - 1) G α - 1 ( y ) , G 1 ( y ) = 1 - e - y P ar ( α, τ ) : f ( x ) = ατ α x - α - 1 U ( x - τ ) P ar ( α, τ ) : F ( x ) = 1 - x τ - α U ( x - τ ) L ( α ) : f ( x ) = α 2 e - α | x | L ( α ) : F ( x ) = 1 2 e αx if x 0 1 2 + 1 2 (1 - e - αx ) if x > 0 = 1 2 e αx (1 - U ( x )) + 1 - 1 2 e - αx U ( x ) N ( m, σ 2 ) : f ( x ) = 1 σ 2 π e - ( x - m ) 2 2 σ 2 σ
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