Unit 2-LT 14-28

Intro to Stats

Relative Frequency

proportion of times the vent occurs out of the total number of trials

P(A)= number of times A occured/number of trials

Contingency Table

P(Red)= (21+26)/(21+26+16+23)=47/86=.547

P(Male and Brown)=23/(21+26+16+23)=23/86=.267

Law of Large Numbers

A procedure or event is repeated more and more times, the relative frequency approached the actual probability.

5% Rule

Rule of thumb for identifying unusual elements of a dataset.

\-Any class or neighboring classes with a total of .05 or less probability is considered unusual

\--Unusually low 0 and 1

\--Unusually high 7

Random Variable

A variable that has a single value for each outcome of an experiment. The value of the random variable is determined by chance by the outcome of the experiment.

Discrete Random Variable

has either a finite or countable number of values. It usually involved whole numbers, no decimals or fractions

Frequency Distribution

Usually present discrete random variable distributions.

Expected Value

of discrete random variable is denoted by E and represents the average of all possible outcomes

(Same as mean)

Classical (theoretical) probability

Used when each outcome in a sample space is equally likely to occur

\-situations that can be mathematically modelled

P(E)=number of outcomes in event E/

Disjoint/mutually exclusive

cannot occur simultaneously

Addition Rule

applies to two or more events that are mutually exclusive

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

\
Example

What is the probability of rolling a die and it landing of 2 or 5?

P(2 or 5)= P(2) +P(5)=1/6+1/6=2/6=.333

Not Mutually Exclusive

Must consider the common outcomes shared by the events

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

Multiplication Rule Example

What is the probability that one student will roll a 2 and another student will roll a 5?

P( 2 and 5)=P(2) x P(5)=1/6x1/6=1/36=.02777=.028

Conditional Probability

When A or B are not independent, denoted P(AlB). This means the probability of A occurring if we know B has happened.

Example

If we know that someone is a Nebraskan, what is the probability they are male?

=P(N MALE)=300/550=5.50

Symbolic Inequalities for Verbal Phrases

Poisson Distribution

Discrete Data

Must be random, must be independent, Uniformly distributed over interbal

Binomial Probability Distribution

Discrete Data

\-each trial has one of two possible outcomes

\-The procedure has a fixed number of trials

\-The trials are independent

\-The probabilities remain constant for all trials

Notation for Binomial Probability Distribution

P(S)=p probability of success

P(F)= 1 -p =q probability of failure

n is the number of trials

s is the number of successes

Continuous Random Variables

Can take on any value between two numbers

\-Typically result from measuring

\-Have infinitely many possible values spread out over an interval with no gaps

\-Usually the probability is 0 because the number of values can be infinite

Normal Distributions

Involve continuous data

Special Characteristics- Bell shapes, symmetric, (mean,median, and mode are all the same)

Tails

The left and right ends of the normal curve

\- never reach the baseline

Special normal called the standard normal distribution

the space between the normal curve and the baseline is equal to one square unit which allows the values of the curve points to equal probabilities for those locations

Normal Distribution

Asks you to determine probabilities of certain values happening within a normally distributed dataset.

Inverse normal distribution problems

the probability of a value or values

Central Limit Theorem

Uses sampling distribution

standard deviation is divided by SQRT

Estimate

A specific value or range of values used to approximate a population parameter

Point Estimate

A single value used to approximate a population parameter

Sampling Distribution

Distribution of estimates over many independent samples from the same population

Confidence Interval

Large number of samples are collected at a certain probability is created for each sample, approximately the required percentage of these intervals will contain the population parameter in question

Determining Sample Size

Use formula n = (z α/2 /(2E))2

ALWAYS round up with decimal