Stats

Question 1

What are E(aX+b) and Var(aX+b) equal to

Answer 1

• aE(X) + b
• a^2Var(X)

Question 2

What are E(aX +- bY) and Var(aX +- bY) equal to

Answer 2

• aE(X) +- bE(Y)
• a^2Var(X) + b^2Var(Y) if X and Y are independent

Question 3

• What are E(X+X) and Var(X+X) equal to

Answer 3

• E(X) + E(X)
• Var(X) + Var(X)
• X + X != 2X when calculating expectation and variance

Question 4

What are the condtitions for a uniform distribution

Answer 4

• Fixed number of outcomes
• Probability of each outcome is the same

Question 5

Derive E(X) and Var(X) for uniform distribution

Answer 5

• Refer to powerpoint on google classroom

Question 6

What are the conditions for a binomial distribution

Answer 6

• Outcomes are success or failure
• Probability of success is constant
• Outcome of each trial is independant of any other trial
• Counting the number of successes from a fixed number of trials

Question 7

What are E(X) and Var(X) in a binomial distribution

Answer 7

• E(X) = np
• Var(X) = npq or np(p-1)

Question 8

What are the conditions for a geometric distribution

Answer 8

• Outcomes are success or failure
• Probability of success is constant
• Outcome of each trial is independant
• Counting the number of trials for the first success to occur

Question 9

What are the conditions for a poisson distribution

Answer 9

• Events occur randomly
• Events occur independetly of one another
• Events occur at a uniform average rate
• Counting the amount of times an event occurs over a given time period

Question 10

What are the desireable features of a sample

Answer 10

• Unbiased
• Representative of the population
• Data should be relevant

Question 11

Why may a sample be neccessary rather than using the whole population

Answer 11

• Population is too large and too expensive to use cencus
• Sampling process may be destructive

Question 12

What are the two advantages of using random samples

Answer 12

• Enables proper inference to be undertaken
• The sample is unbiased

Question 13

What is the condition for poisson distribution to be valid if binomial distribution is valid

Answer 13

• n is large and p is small

Question 14

What is crucial for a PMCC hypothesis test to be valid

Answer 14

• The underlying population must have a bivariate normal distibution
• Eliptical shape of data

Question 15

Where would spearmans rank be viable rather than PMCC

Answer 15

• Not from a bivariate normal distibution
• Not random on random
• Non-Linear correlation (assotiation)

Question 16

What is the consequence of estimating the paramter of poisson in a goodness of fit test

Answer 16

• Take one from the degrees of freedom

Question 17

What is the relationship between an x on y and y on x regression line

Answer 17

• both pass through (x bar, y bar)

Question 18

List the conditions for effect sizes

Answer 18

• Small 0.1
• Medium 0.3
• Large 0.5

Question 19

When can two poisson distributions be added

Answer 19

• When the two variables are independent

Question 20

When would taking into account effect sizes be viable

Answer 20

• When the data set is large

Question 21

How do you calculate the effect size of your PMCC test

Answer 21

• Square PMCC

Question 22

How do you calculate a residual

Answer 22

• Observed - Calculated
• y - (a + bx)

Question 23

What does the coefficient of determination tell us

Answer 23

• The proportion of variation in y that is explained by the variation in x

Question 24

What happenes to degrees of freedom in a goodness of fit test

Answer 24

• 1 is taken away automatically

Question 25

What is the p-value compared with

Answer 25

Siginificance level