Statistics

Question 1

Goodness of fit for Poisson distribution

Answer 1

H0: modelled by Poisson
H1: not modelled by Poisson 
Find mean
X | P(X=x) | n x P(X=x) | fe
V = classes - parameters -1
X^2 > critical value
Reject H0

Question 2

Geometric distribution

Answer 2

Number of trials till success
Same probability 
P(X=r) = q^r-1 x p
Ex = 1/p
Varx = 1-p / p^2

Question 3

Residual equation

Answer 3

Y1 - (a + bx1)

Question 4

Spearman’s rank

Answer 4

Rs = (1 - 6 sum di^2) / n(n^2 - 1)

Association

Question 5

Ex and varx of function X

Answer 5

E(g[x]) = integral g[x]f(x)dx 
Var(g[x]) = integral (g[x])^2 f(x)dx - (E(g[x]))^2

Question 6

X + Y Poisson

Answer 6

X + Y distributed Poisson( x + u)

Question 7

Goodness of fit for binomial

Answer 7

H0: can be modelled 
H1: not modelled 
Find n and p
Fe is less than 5 merge cells
If X^2 > critical value 
Reject H0

Question 8

What critical values for a Wilcoxen

Answer 8

For two tailed take smaller one
One tailed , test if population mean is greater than M take W- and W+ for population mean less than M

Accept H1 if W is less than or equal to critical value

Question 9

When using a cdf how do you find area between two points

Answer 9

Take away Fx - Fx1

Question 10

Median for cdf

Answer 10

Fm = 0.5

Question 11

What is the uniform distribution

Answer 11

Same distribution over value

Question 12

Proof for ex of uniform

Answer 12

N+1 /2

Question 13

Proof of variance of uniform

Answer 13

N^2 -1 /12

Question 14

Describe geometric distribution

Answer 14

Probability of a success and not a success