Distributions

Question 1

Mean of poisson

Answer 1

μ

Question 2

Variance of poisson

Answer 2

μ

Question 3

Mean of bernoulli

Answer 3

θ

Question 4

Variance of bernoulli

Answer 4

θ(1-θ)

Question 5

Mean of binomial

Answer 5

n*p

Question 6

Variance of binomial

Answer 6

npq

Question 7

Mean of multinomial for Xi

Answer 7

n*pi

Question 8

Variance of multinomial for Xi

Answer 8

npiqi

Question 9

Covariance between Xi and Xj

Answer 9

npipj

Question 10

Mean of uniform

Answer 10

(α + β) / 2

Question 11

Variance of uniform

Answer 11

(β - α)^2 / 12

Question 12

Mean of beta

Answer 12

α / (α + β)

Question 13

Variance of beta

Answer 13

(α / (α + β)) * (β / (α + β)) * (1 / (α + β + 1))

Question 14

Mean of gamma

Answer 14

α / β

Question 15

Variance of gamma

Answer 15

α / β^2

Question 16

Mean of exponential

Answer 16

1/λ

Question 17

Variance of exponential

Answer 17

1 / λ^2

Question 18

Conjugate prior for θ when y ~ binomial

Answer 18

Beta

Question 19

Conjugate prior for θi,..,θk when y ~ Multinomial

Answer 19

Dirichlet

Question 20

Conjugate prior for θ when y ~ poisson

Answer 20

Gamma

Question 21

Conjugate prior for θ when y ~ exponential

Answer 21

Gamma

Question 22

Conjugate prior for θ when y ~ Uniform

Answer 22

Pareto

Question 23

Conjugate prior for μ when y ~ Normal and σ^2 known

Answer 23

Normal

Question 24

Conjugate prior for σ^2 when y ~ Normal and μ known

Answer 24

Inverse gamma

Question 25

Conjugate prior for σ^2 and μ when y ~ Normal

Answer 25

Inverse gamma conditional normal