Distributions

Question 1

Exponential Distribution PDF

Answer 1

f(x,λ) = λe^(-λx), x≥0

Question 2

Exponential Distribution CDF

Answer 2

F(x, λ) = 1 - e^(-λx), x≥0

Question 3

What transformation makes a Gamma distribution?

Answer 3

The sum of n X~EXP(β) ~GAM(n,β)

Question 4

What form of Gamma follows a Chi-Square Distribution?

Answer 4

X~GAM(k/2, 2) <=> X~χ(dof = k)

Question 5

What is the distribution of the sum of a Gamma function GAM(α(i), β)?

Answer 5

ΣX(i) ~ GAM(α(1) + α(2) + … + α(n), β)

Question 6

X(1) ~GAM(α(1), β
X(2) ~GAM(α(2), β

What is distribution of X(1)/(X(1) + X(2))?

Answer 6

Beta(α(1), α(2))

Question 7

Normal Distribution PDF

Answer 7

f(x, µ, σ) = 1/sqrt(2πσ^2)e^(-0.5((x-µ)/σ)^2)

Question 8

Uniform Distribution PDF

Answer 8

f(x) = 1/(b-a) , x∈[a,b]

Question 9

Uniform Distribution CDF

Answer 9

F(x) = (x-a)/(b-a), x∈[a,b]

Question 10

Y = X1^2 + … +Xk^2, Xi~N(0,1)

Answer 10

Y~GAM(k/2, 2) = chi-square(k)

Question 11

X~N(mu, sigma^2)

e^X?

Answer 11

~logN(mu, sigma^2)

Question 12

X~N(0,1)
Y~chi-square(k)

X/sqrt(Y/k)

Answer 12

t(k)

Question 13

F-distribution from other r.v.

Answer 13

(Z1/k1)/(Z2/k2)

Z1~chi-square(k1)
Z2~chi-square(k2)