math ch10: probabilities and statistics

measures how likely it is for an event to occur

probability for any event X is denoted by

the probability of an impossible event is

the probability of a certain event is

formula of probability

the probability of an general event is

probability gained by gathering data from observation

each observation is a

formula for probability of an event in experiment

if an event M can occur in m ways and is followed by an event N that can occur in n ways, then event M followed by event N can occur in (result and name )

writing 3! is called

factorial n! is equal to

0!

1!

2!

3!

4!

5!

5! can be rewritten as

permutation

the number of different permutations of n objects where there are rk repeated times

rule of repeated permutation

if n objects are arranged in a circle without a reference point, then there are—-permutations

if n objects are arranged in a circle with a fixed reference point, then there is —-permutations

combinations

when the occurence of one event affects how a second event can occur, the events are

if they do not affect each other, the events are

probability of A and B (dependent)

example of independent probability

probability of A and B (dependent)

example of dependent probability

the probability that an event B will occur given that another event has already occurred is called

formula for P(B/A)

two events that have common outcomes are called

two events that cannot happen at the same time

probability of A or B (mutually exclusive)

examples of mutually exclusive probability

probability of A or B (mutually exclusive)

example of mutually exclusive probabilities

when are two events said to be complementary

probabilities of two complementary events add up to

P(A) + P(A~)=

all members of a set

part of a population

you can get statistical information about population by

types of statistical studies (name)

to observe members of a sample in such a way they are not affected by the study

to divide a sample into groups then impose a treatment on one group but not on the other control group. then to compare the effect on the treated group to the controlled group

margin of error formula

the margin of error helps in estimating a ———- percentage of the whole population by giving a ——————

measures of central tendency (name)

mean formula

when do we use mean

median formula

when do we use mean

mode formula

when do we use mode

measures of dispersion (name)

sigma represents +rule

sigma squared represents + rule

x bar or mu represents + rule

range is

standard deviation

when the measure of dispersion is low, it means that data values are

refers to a longer or fatter tail on the left side of the distribution

refers to a longer or fatter tail on the right

both skewers refer to

this distribution has no skew

has data that vary randomly from the mean

the graph of a normal distribution is represented by

the binomial theorem tells us how to

instead of using the binomial theorem, we can use

nCr, where n and r mean

the exponent of x starts from n then ———by ———— till———- while the exponent of y starts from ——- then ——- till —— by —-

the sum of the exponents is always equal to

any exponent is applied on the

the number of terms is

to determine a term after expanding binomial expression in the form (x+y)^n, let: Px, Py, a, and n represent:

Px=

Py=

it is frequently used to model the number of successes or failures in a sample size n

n is

p is

q is

p+q=

mean=

variance=