Probability

Question 1

what is probability?

Answer 1

a numerical measure of how likely an event will occur, it involves measuring uncertainty

Question 2

how can probability be used in statistical inference?

Answer 2

e.g.

what does the sample data tell us about the whole population

likelihood it will happen etc everyone

try to infer from our sample to a whole population

Question 3

how is probability used in a business setting?

Answer 3

business statistics apply mathemetauical formulas or models to business information in an attempt to determine the probability of success relating to an opportunity

• will new service delivery improve customer satisfaction?

Question 4

what do probabilities range from?

Answer 4

0 to 1
0 = impossible
1 = certain

sometimes expressed as percentages or odds

Question 5

what are the sources of probability?

Answer 5

• subjective
• classical (theoretical)
• empirical (statistical)

Question 6

what is subjective probability?

Answer 6

the liklihood (probability) of a particle event happened that is assigned by an indidvudal based on whatever info is available

• if there is little or no past experience or info then probability maybe arrived subjectively
• sole based on intuition of a person
• more of an opinion (likihod you will be married by 30)

Question 7

what is classical (theoretical) probability?

Answer 7

• all outcomes are equally likely
• probability is a logical thing

prob = number of favourable outcomes / number of possible outcomes
such as flip a coin 1/2 going to be a head

Question 8

what is empirical (statistical) probability?

Answer 8

• based on experiments
• relative frequency, proportion of times the outcome has occurred over many repetitions
• e.g. rained 200 days last year so prob = 200/365

Question 9

Key words for prob

experiment?

Answer 9

an action/process with a well defined set of outcomes, on any single repetition on and only one of the possible outcomes will occur

Question 10

key words

sample space? (S)

Answer 10

set of all possible outcomes

Question 11

key words

element?

Answer 11

a specific outcome

e.g. coin toss there are two interchnagble elements

Question 12

key word

event?

Answer 12

subset of the sample space
it may be a specific outcome or combination of outcomes

landing on heads is the event

Question 13

key words

probability of an event?

Answer 13

sum of all probabailties of all elements that make up the event

Question 14

how many rules are there of probability?

Answer 14

four

two with a specific and general case

Question 15

what is addition rules?§

Answer 15

with two event A and B we are interested in the probbailtu of event A OR B

Question 16

what is the specific rules for addition?

Answer 16

are the events mutually exclusive
YES
P(A or B) = P(A) +P(B)

Question 17

what is the general rule for addition?

Answer 17

events are not mutually exclusive, elements in common

P(A or B) = P(A) + P(B) - P(A and B)

Question 18

what are multiplication rules? AND

Answer 18

with two events A and B, we are interested in the probability of event A AND event B

Question 19

with multiplication rule what do you do if the to events are indepentnat ?

Answer 19

use specific rule

= P(A and B) = P(A) x P(B)

Question 20

with multiplication rule what do you do if the two events aren’t independent?

Answer 20

General rule
chance that event B is influenced by event A

= P(A and B) = P(A) x P(B/A)

P(B/A) = conditional probability of event B given that event A has already happened

Question 21

what is probability distribution?

Answer 21

table/euation that links each outcome of a statistical experiment with its probability of occurance

Question 22

what is a statistical experiment?

Answer 22

• can have more than one outcome
• each outcome can be specified in advance
• outcome depends on chance
  e. g. a coin toss

Question 23

what is a variable

Answer 23

a symbol that can take any of a specified set of values

x y

Question 24

what is a random variable?

Answer 24

when the value is the outcome of a statistical experiment that variable is a random variable

Question 25

what is uniform probability distribution?

Answer 25

all values of a rsandom variable occur with equal probability
(dice toss each variable = 1/6)
chance that 5 will get picked = P(X=5)=1/6

Question 26

what is a continuous variable?

Answer 26

infinite

variable can take any value between 2 specified values e.g. height between 1 - 2 m

Question 27

what is a discrete variable?

Answer 27

finite heads or tails
throw four times
can be any integer between 0-4 but not any number between 0-4
can throw a head 2.5 times

Question 28

wha is difference about discrete and continuous prob distribution?

Answer 28

continuous can’t be shown in tabular form

Question 29

what is normal distribution?

Answer 29

most important example of a conitnous probability distribution

dependant on the mean (position of distribution)
and standard deviation (larger = flatter)

all ND look symmetrical, bell shaped

Question 30

what implications for probability does normal distribution have?

Answer 30

• total area under normal curve is equal to 1
• probabailt that a normal random variable X equals any particular value is 0
• if you shade in the part you can see the probability of it being more or less than a particular area