Probability Distributions

Question 1

Measures of central tendency

Answer 1

• mean
• weighted mean
• mode
• midrange
• median
• modal class

Question 2

Measures of spread

Answer 2

• range
• interquartile range
• standard dev
• variance

Question 3

Measures of position

Answer 3

• median
• quartiles

Question 4

Standard dev formula

Answer 4

Root : Sxx/n-1

Question 5

Expectation of DRV

Answer 5

E(X) = Sum of r * P(X=r)

Question 6

Variance of DRV

Answer 6

Var(X) = E(X2) - (E(X)) 2

Question 7

Another method for var of DRV

Answer 7

Var(X) = (r-U)2 * P(X=r)

Question 8

Expectation: general results

Answer 8

• E(aX+b) = aE(X) + b
• E(cX) = cE(X)
• E(d) = d

Question 9

Variance: general results

Answer 9

Var(aX) = a2 Var(X)
Var (aX+b) = a2 Var(X)
Var (c) = 0

Question 10

Standard dev: general results

Answer 10

• if (X) turns into (aX) = variance increases by a2 but standard dev increases by sf of only a

Question 11

Combining: general results

Answer 11

E (X1 + X2) = E(X1) + E(X2)
E (X1 - X2) = E(X1) - E(X2)
Var (X1 + X2) = Var(X1) + Var(X2)
Var (X1 - X2) = Var(X1) + Var(X2)

Question 12

Linear combinations

Answer 12

E(aX+bY) = aE(X) + bE(Y)
Var(aX+bY) = a2 Var(X) + b2 Var(Y)

Question 13

Binomial distribution formula

Answer 13

P(X=r) = nCr * (p)r * (q)1-r

Question 14

Binomial E(X) and Var(X)

Answer 14

E(X) = np
Var(X) = npq

Question 15

When is binomial used

Answer 15

• fixed number of trials (n)
• each trial can be classified as a success or failure
• independent events
• same prob of success (p)

Question 16

Poisson distribution formula

Answer 16

P(X=r) = (e-λ * λr )/r!

Question 17

Poisson E(X) and Var(X)

Answer 17

• given in the question and must change when given a different time interval

Question 18

When is poisson used

Answer 18

• variable occurs in a fixed interval of time or space
• occurs randomly
• events occur independently of each other
• mean number of times occurring is same in each interval

Question 19

If λ small..

Answer 19

Has a positive skew and as λ increases, becomes more symmetrical

Question 20

Sum of Poisson distribution

Answer 20

• assuming two events are independent, T = X + Y
  Where = P(T=r) = P(X=r) + P(Y=r) where T = λ1 + λ2

Question 21

Links between poisson and binomial

Answer 21

• when n very large and p small - can be used interchangeably and have similar results

Question 22

Uniform distribution

Answer 22

1/n

Question 23

Uniform E and Var

Answer 23

E(X) = n+1/2
Var(X) = n2 -1 /12

Question 24

Uniform formulas…

Answer 24

Can only be used if k starts with 1

Question 25

Geometric distribution graph

Answer 25

Will always decrease as increases so, no normal uniform dis

Question 26

In geo, P(X>10)

Answer 26

(1-p) ^10

Question 27

Geo : P(X<10 )… NORMAL

Answer 27

1 - (q) ^ 9

Question 28

In geo.. most likely

Answer 28

Will always be largest number as gets smaller as n increases

Question 29

Geo E and Var

Answer 29

E(X) = 1/p Var (X) = 1-p/p2

Question 30

PMCC requirements

Answer 30

- bivariate normal dis - elliptical shape - random/ independent variable - measures correlation - linear data

Question 31

PMCC form

Answer 31

r = Sxy/ root Sxx * Syy

Question 32

PMCC as a test stat

Answer 32

Ho: p =0 H1: p <> not 0

Question 33

If PMCC greater or less.. than critical

Answer 33

If less, then Ho accepted and can see no correlation. If greater, than much greater and can see Corre

Question 34

PMCC as effect size

Answer 34

r = 0.1 is small effect size and…

Question 35

Rs measure

Answer 35

- measures association NOT corre - not linear

Question 36

Rs as test stat

Answer 36

Ho: There is not association… H1: There is an assoc

Question 37

Rs

Answer 37

Rs = 1 - 6di2/ n(n2-1)

Question 39

Use of significance level and meaning of x%

Answer 39

Sig level is the probability the rejecting the null hyp when it in fact is true. X% means that if there is no association between x and y, only x out of 100 would lead to thr conclusion that there is an association between x and y

Question 40

Often questions for least reg

Answer 40

Estimate values and comment on reliability due to inter/extrapolation

Question 41

Often questions asked in chi: what has to be followed for chi

Answer 41

Sample has to be random

Question 42

Goodness of fit for a reg line

Answer 42

Measure PMCC 2

Question 43

Advantage and dis of x% sig level

Answer 43

Ad - it is less likely to reject null when it is in fact true Dis - it is more likely to accept null when it is in fact false

Question 44

B and Po used if..

Answer 44

N is large - n>50 p is small - p<0.2

Question 45

When can geometric be used

Answer 45

FICT C - is continued until success