Probability Flashcards
what is probability?
a numerical measure of how likely an event will occur, it involves measuring uncertainty
how can probability be used in statistical inference?
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
how is probability used in a business setting?
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?
what do probabilities range from?
0 to 1
0 = impossible
1 = certain
sometimes expressed as percentages or odds
what are the sources of probability?
- subjective
- classical (theoretical)
- empirical (statistical)
what is subjective probability?
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)
what is classical (theoretical) probability?
- 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
what is empirical (statistical) probability?
- 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
Key words for prob
experiment?
an action/process with a well defined set of outcomes, on any single repetition on and only one of the possible outcomes will occur
key words
sample space? (S)
set of all possible outcomes
key words
element?
a specific outcome
e.g. coin toss there are two interchnagble elements
key word
event?
subset of the sample space
it may be a specific outcome or combination of outcomes
landing on heads is the event
key words
probability of an event?
sum of all probabailties of all elements that make up the event
how many rules are there of probability?
four
two with a specific and general case
what is addition rules?§
with two event A and B we are interested in the probbailtu of event A OR B
what is the specific rules for addition?
are the events mutually exclusive
YES
P(A or B) = P(A) +P(B)
what is the general rule for addition?
events are not mutually exclusive, elements in common
P(A or B) = P(A) + P(B) - P(A and B)
what are multiplication rules? AND
with two events A and B, we are interested in the probability of event A AND event B
with multiplication rule what do you do if the to events are indepentnat ?
use specific rule
= P(A and B) = P(A) x P(B)
with multiplication rule what do you do if the two events aren’t independent?
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
what is probability distribution?
table/euation that links each outcome of a statistical experiment with its probability of occurance
what is a statistical experiment?
- can have more than one outcome
- each outcome can be specified in advance
- outcome depends on chance
e. g. a coin toss
what is a variable
a symbol that can take any of a specified set of values
x y
what is a random variable?
when the value is the outcome of a statistical experiment that variable is a random variable
what is uniform probability distribution?
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
what is a continuous variable?
infinite
variable can take any value between 2 specified values e.g. height between 1 - 2 m
what is a discrete variable?
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
wha is difference about discrete and continuous prob distribution?
continuous can’t be shown in tabular form
what is normal distribution?
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
what implications for probability does normal distribution have?
- 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
