Question 1

E(X)

Accepted Answer

Σx*p(X=x)

Question 2

Var(X)

Accepted Answer

E(X^2)-E(X)^2. Same as average difference of term from mean, squared, and is standard deviation squared

Question 3

E(a+bX)

Accepted Answer

a+bE(X)

Question 4

Var(a+bX)

Accepted Answer

b^2Var(X)

Question 5

E(X+Y)

Accepted Answer

E(X) + E(Y)

Question 6

E(a+bX + c + dY)

Accepted Answer

(a+c) + bE(X) + dE(Y)

Question 7

Var(X+Y)

Accepted Answer

Var(X) + Var(Y)

Question 8

Signs of E and Var when combining variables

Accepted Answer

For E, + or - depending on sign inside. For Var, always add the variance even for Var(X-Y).

Question 9

How to derive mean of uniform

Accepted Answer

All probabilities are 1/n so 1/n can be taken out of the Σ function. Then the result (n)(n+1)/2 can be times by 1/n to give (n+1)/2

Question 10

How to derive variance of uniform

Accepted Answer

E(X^2) can again take 1/n out of Σ, use result for Σr^2 then divide by n. E(X)^2 from before.

Question 11

Situation for binomial

Accepted Answer

Fixed chance of success.
Independent
Fixed no trials
Binary outcome (Success or failure)

Question 12

Derivation for mean of binomial.

Accepted Answer

The expectation of a given trial is 1*p + 0*q = p. Using the The outcome, X, is equal to the sum of x1+x2+x3 where E(xn)=p, so E(X)=np by the rule that E(X+Y)=E(X)+E(Y)

Question 13

Derivation for the Variance of binomial

Accepted Answer

Again, the variance of 1 trial is easy. E(X^2)-E(X)^2. == p-p^2 = p(1-p) = pq. The variance of X is the variance of n trials each with variance pq, so total is npq

Question 14

Difference between Var(nX) and Var (X + X + X + X... n times)

Accepted Answer

Var nX is the variance of one sample times by n, so the variance will be n^2VarX. For the other, it is like taking n samples, each of which being random, so the total is less varied, Hence nVarX

Question 15

Situation for Poisson

Accepted Answer

Constant average rate (over distance or time) in a fixed interval, independently of each other. Like phone calls or defectives. Also only suitable if mean approx= variance as model assumes same.

Question 16

When are both binomial and Poisson appropriate

Accepted Answer

When bin is appropriate AND n is large AND p is small. np must be less than 5.

Question 17

Sum of two Poisson

Accepted Answer

Also Poisson, with lambda=sum of other two as long as they were independent.

Question 18

Geometric distribution

Accepted Answer

Repeated trials until success. Separate trials have to be independent, fixed probability of success and binary.

Question 19

Calc geo probabilities

Accepted Answer

Calc can do for cumulative, but for general, p(X=x) is x-1 failures and 1 success, so is p(q^(x-1))

Question 20

Meaning of bivariate data

Accepted Answer

Two sets of data in which each datum from one set is paired with one from the other

Question 21

Types of bivariate

Accepted Answer

Random on non-random. One is independently varied and the other is measured.
Random on random. Two random variables with a proposed relationship are compared.

Question 22

Significance of the type

Accepted Answer

For random on non random, the independent variable is considered to have negligible error, so no variance. On a scatter diagram, its data will lie on fixed lines.

Question 23

When is PMCC valid for hypothesis testing?

Accepted Answer

Only for random-on-random as the p values assume two normally distributed data sets. Bivariate normally distributed data.

Question 24

How to calculate PMCC on calculator

Accepted Answer

Data in 2 lists. CALC REG X ax+b

Question 25

What is PMCC for

Accepted Answer

Linear association/ Correlation.

Question 26

Effect size for pmcc

Accepted Answer

The effect one variable has on another. The higher abs(r) is, the greater the effect size.

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