The Different Distributions

Question 1

Conditions for Binomial Distribution

Answer 1

Fixed number of trials
Independent trials
Constant probability of success
Two outcomes

Question 2

Binomial P(X=x)

Answer 2

nCr p^r (1-p)^n-r

Question 3

Binomial Expected Value

Answer 3

E(X) = np

Question 4

Binomial Variance

Answer 4

Var(X) = np(1-p)

Question 5

Conditions for Poisson

Answer 5

Random events
Independent Events
Constant rate of occurring

Question 6

Poisson P(X=x)

Question 7

What can happen if you have two independent poisson distributions?

Answer 7

X + Y - Po(X1 +X2)

Question 8

What can happen if your n is too large and p too small in binomial?

Answer 8

can turn into poisson distribution

Question 9

Poisson Expectation

Answer 9

E(X) = λ

Question 10

Poisson Variance

Answer 10

Var(X) = λ

Question 11

Conditions for Geometric

Answer 11

only 1 successful outcome

Question 12

Geometric P(X=x)

Answer 12

(1-p)^x-1 (p)

Question 13

Geometric Expectation

Answer 13

E(X) = 1/p

Question 14

Geometric Variance

Answer 14

1-p/ p2

Question 15

Geometric P(X>x)

Answer 15

(1-p)^x

Question 16

Geometric P(X<r)

Answer 16

1-(1-p)^x-1

Question 17

Conditions for Discrete Uniform Distribution

Answer 17

fixed number of equally occuring trials

Question 18

Uniform P(X=x)

Answer 18

1/n

Question 19

Uniform Expectation

Answer 19

n+1 /2

Question 20

Uniform Variance

Answer 20

(n+1)(n-1) / 12