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26 Cards in this Set

  • Front
  • Back

Uniform distribution, U(N)



p(x) = ?

p(x) = 1/N



x = 1, 2, ..., N

Uniform distribution, U(N)



Mean / E[X] = ?

E[X] = (N + 1) / 2

Uniform distribution, U(N)



Variance / Var[X] = ?

Uniform distribution, U(N)



MGF / MX(t)

Binomial Distribution B(n, p)



p(x) = ?

Binomial Distribution B(n, p)



mean / E[X] = ?

E[X] = np

Binomial Distribution B(n, p)



Var[X] = ?

Var[X] = npq

Binomial Distribution B(n, p)



MGF / Mx(t)

Poisson Distribution with parameter λ



p(x) = ?

x = 0, 1, 2, ...

x = 0, 1, 2, ...

Poisson Distribution with parameter λ



mean / E[X] = ?

E[X] = λ

Poisson Distribution with parameter λ



Var[X] = ?

Var[X] = λ

Poisson Distribution with parameter λ



MGF / Mx(t) = ?

Geometric distribution 0 < p < 1



p(x) = ?

Geometric distribution 0 < p < 1



Mean / E[X] = ?

E[X] = q / p

Geometric distribution 0 < p < 1



Var[X] = ?

Geometric distribution 0 < p < 1



MGF / Mx(t)

Negative Binomial



(X = # of failures till the r-the success)



p(x) = ?

Negative Binomial



(X = # of failures till the r-the success)



mean / E[X] = ?

Negative Binomial



(X = # of failures till the r-the success)



Var[X] = ?

Negative Binomial



(X = # of failures till the r-the success)



MGF / Mx(t) = ?

Hyper-geometric


{M objects, K of type 1, M - K of type 2}


{n = # of objects chosen, x = # of type 1}



p(x) = ?

x ≤ min[n, K]

x ≤ min[n, K]

Hyper-geometric


{M objects, K of type 1, M - K of type 2}


{n = # of objects chosen, x = # of type 1}



mean / E[X] = ?

Hyper-geometric


{M objects, K of type 1, M - K of type 2}


{n = # of objects chosen, x = # of type 1}



Var[X] = ?

Multinomial Distribution


{n, p1, p2, ..., pk}



p(x) = ?


x1 + x2 + ... + xk = n

x1 + x2 + ... + xk = n

Multinomial Distribution


{n, p1, p2, ..., pk}



Mean / E[X] = ?

Multinomial Distribution


{n, p1, p2, ..., pk}



Var[X] = ?