Probability test 2

Probability Experiment

One in which we don’t know an individual outcome, but we know how long a series of repetitions will come out

Probability

Proportion an event occurs in the long run as a probability experiment is repeated

Sample Space

contains all possible outcomes for a probability experiment

Event

outcome or collection of outcomes from a sample space

Probability Model

consists of a sample space along with the probability of each event

P(A)

number of outcomes in A / Number of outcomes in sample space

Independent Event

occurence of 1 event does not affect the occurence of another

Dependent Event

occurence of 1 event affects the other

Mutually Exclusive Events

condition where it is impossible for both events to occur at the same time

Conditional Probability Formula

p(a and b)/p(a)

Joint Probability formula (AND) for independent events

p(a) * p(b)

Joint Probability for dependent events (AND)

p(a) * p(b|a)

Union probability for Independent events (OR)

p(a) + p(b)

union probability for independent events

p(a) + p(b) - p(a and b)

Conditions for a binomial distrobution

• fixed number of trials

• 2 possible outcomes (success or failure)

• independent trials

• p(success) is the same during each trial

• random variable x represents number of successes

Random Variable

unique outcome of a probability experiment

Discrete Random Variable

random variables whose values can be listed

Continuous Random Variable

random variables that can take on any value in an interval

symbol for # of trials in a binomial distrobution

n

symbol for probability of success in binomial distrobution

P

Symbol for failure in a probability distrobution

Q or 1 - P

Possion Distrobution

Describes certain events that occur in time or space

Conditions for a Possion Distrobution

• avg rate of change at which events occur is always the same

• number of events that occurs in non-overlapping time intervals are independent

• for a very short interval of time t:

  • its impossible for more than 1 event to occur within the time interval

  • p(one event) in the interval is the average rate of change * time

Probability Density Curve

Curve used to describe the distribution of a continuous random variable