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

Question 13

Assumptions for PMCC hypothesis test

Answer 13

data must be bivariate normal.
Random on random.
Scatter diagram should be elliptical without skew or bimodalness
data is linear
data is without outliers

Question 14

Explain effect size

Answer 14

For large values of n even a small non zero PMCC value will lead to a rjection of the null hypothesis so use a general rule insted.

Question 15

How to calculate degrees of freedom

Answer 15

Number of rows - 1, number of columns - 1
if just one row then just n - 1
if yiu had to estimate a variable for a poission or binomial goodness of fit test then you minus 1 again