Lecture 4 - probability distributions

Question 1

what is bayesian probability?

Answer 1

degree to which an individual believes an event will happen

Question 2

what is relative frequency interpretation?

Answer 2

the number of times the event will take place over the long run

Question 3

what are key features of relative frequency probabilities

Answer 3

1. can be repeated and the outcome can be observed
2. settles down to one value over a long run
3. cannot be used to determine a single event

Question 4

what is the addition rule?

Answer 4

if the events are mutally exclusive you add them together

Question 5

what is the multiplication rule?

Answer 5

if the events are independent you multiply them together

Question 6

what is the mean of a probability distribution?

Answer 6

average value in the long run

expected value

Question 7

what is the standard deviation of a probability distribution?

Answer 7

amount of variation about the mean

Question 8

what is binomial distribution used for?

Answer 8

discrete variables
the distribution followed by the number of successes in n independent trials when the probability of any single trial being a success is p

Question 9

how can mean and standard deviation be measured in binomial distribution?

Answer 9

Mean = np

Standard deviation = √(np(1-p))

Question 10

what is normal distribution used for?

Answer 10

Probability distribution for continuous variables

Question 11

how can you find out the proportion of observations between two limits?

Answer 11

finding the area under the curve between two points

Question 12

what are the features of standard normal distribution?

Answer 12

mean of 0 and SD of 1

Question 13

where does 95% of the data in a normal distribution fall?

Answer 13

within two standard deviations of the mean

Question 14

where does 99.7% of the data fall in a normal distribution?

Answer 14

within 3 standard deviations of the mean

Question 15

what happens to a normal distribution graph when the mean increases

Answer 15

shifts to the right

Question 16

what happens to a normal distribution graph when the standard deviation increases

Answer 16

the graph becomes flatter and closer to the x-axis

Question 17

what happens to the normal distribution graph when standard deviation decreases

Answer 17

the graph becomes longer and points become closer together

Question 18

how is the normal distribution summarised?

Answer 18

X-N( mean , variance )

Question 19

When does the binomial distribution tend towards the normal distribution?

Answer 19

as n(sample size) increases
if np and n(1-p) both exceed 1

Question 20

what can you do when the binomial distribution tends towards the normal?

Answer 20

you can approximate the binonomial distribution using the normal distribution

Question 21

what is the central limit theorem?

Answer 21

If we have a series of independent observations which are identically distributed, their sum tends towards a Normal distribution as the number of observations increases.
It enables us to deduce that the mean of any large series of observations follows a Normal distribution.