Chapter 2 Flashcards
Discrete uniform PMF
f(x) = P(x=x) = 1/b-a+1
Discrete uniform mean
E(x) = (a+b)/2
Discrete uniform VAR
VAR(x) = (b-a+1)^2-1/12
Binomial PMF
f(x) = P(x=x) = nCx · p^x · (1-p)^(n-x)
Mean binomial
E(x) = n · p
Binomial VAR
VAR(x) = n · p · (1-p)
Special property binomial
Sum of independents binomials with the same p equals B(n_i, p)
Hypergeometric PMF
f(x) = P(x=x) = (mCx) · (N-mCn-x)/(Ncn)
Mean hypergeo
E(x) = n · (m/N)
Var hypergeo
VAR(x) = ((n · m)/N) · ((N-m)/N) · (N-n/N-1)
PMF geometric
f(x) = P(x = x) = (1-p)^x-1
E(x) geo
E(x) = 1/p
geometric VAR(x) =
1-p/p^2
PMF geo fails
f(x)=P(x = x) = (1-p)^y · p
Mean geo fails
E(y) = (1/p)-1
Var geo fails
(1-p)/(p^2)
Special property geometric
(x-c|x > c)~X
(y-c|y e c)~Y
Negative binomial PMF
f(x) = P(x = x) = (x-1)C(r-1) · p^r · (1-p)^x-r
Mean negative binomial
r/p
VAR negative binomial
r · ((1-p/p^2)
Negative binomial fails PMF
f(x) = P(x = x) = (y+r-1)C(r-1) · p^r · (1-p)^y
Negative binomial fails mean
(r/p) - r
Negative binomial fails VAR
r((1-p)/p^2)
Special property negative binomial
Somme des binomiales négatives indépendantes X~N.B. (r_i, p)
PMF Poisson
f(x) = P(x = x) = (e^- λ) · (λ^x) / x!
E(x) Poisson
λ