distributions

Question 1

Bernoulli distribution?

Answer 1

PX(0) = 1-p
PX(1) = p
E(X) = p
Var(X) = p(1-p)

Question 2

Binomial distribution?

Answer 2

n>=1
PX(k) = (n k)p^k * (1-p)^n-k
E(X) = np
Var(X) = np(1-p)

Question 3

Geometric distribution?

Answer 3

PX(k)=p(1-p)^k-1
E(X) =1/p
Var(X) = 1-p / p^2

Question 4

Poisson distribution?

Answer 4

λ>0
PX(k) = (λ^k)/k! *e(-λ)
E(X) = λ
Var(X) = λ

Question 5

Negative binomial distribution?

Answer 5

k>=1
PX(n) = (n-1 k-1) p^k * (1-p)^n-k
E(X) = k/p
Var(X) = k* (1-p)/p^2

Question 6

Hypergeometric distribution?

Answer 6

N>=1
Na>=0
n>=1
PX(k) = (Na  k)*(N-Na  n-k)/(N  n)
E(X) = nNa/N
Var(X)=(N-n / N-1)*n*(Na(N-Na)/N^2)

Question 7

Uniform distribution?

Answer 7

a

Question 8

Normal distribution?

Answer 8

u real
s^2>0
fX(t) = (1/sqrt(2pi*s^2))*e(-(t-u)^2/2s^2)
E(X)=u
Var(X)=s^2