distribution formulas

Question 1

Conditions for binomial

Answer 1

fixed number of trials
independent of each other
constant probability of siuccess
two outcomes

Question 2

Expectation and variance of binomial

Answer 2

E(X) = np
Var(X) = np(1-p)

Question 3

conditions for poission

Answer 3

Random rate of occurcence
independent
uniform average rate of occurence

Question 4

Expectation and variance of poission

Answer 4

Lambda for both

Question 5

Formula for poission distribution

Answer 5

x !

Question 6

conditions for the geometric

Answer 6

When there is a number of independent trials until a success is achieved
two outcomes

Question 7

p(X=x) for geometric distribution

Answer 7

(1-p)^x-1 x p

Question 8

P(X <= x) For geometric

Answer 8

1 - (1 - p) ^x

Question 9

expectation and variance

Answer 9

E(X) = 1 / P
Var(X) = 1 - p / p²

Question 10

when to use uniform distribution

Answer 10

When there is an equally likely number of outcomes

Question 11

Expectation and variance of a uniform distribution

Answer 11

E(X) = n + 1 / 2

Var(X) = ( n + 1)(n - 1) / 12

Question 12

proof of uniform distribution expectation and variance

Answer 12

dede