Unit 4 Review

a chance process that is a number between 0 and 1

imitation of a chance behavior, based on a model that accurately reflects

1. State: Ask a question of interest

2. Plan: Describe how to use chance to imitate one reptation of the process

3. Do: Perform many repetitions of the simulation

4. Conclude: Use results of simulation to answer question of interest

the set of all possible outcomes

a description of some chance process that consists of a sample space S and a probability for each outcome

is any collection of outcomes from some chance process; a subset of the sample space

Probability is always a number from 0 to 1, if S is the sample space in a probability model P(S)=1), and P(A) = the number of outcomes corresponding to event A / the total number of outcomes in the sample space

P(A^c) = 1 - P(A)

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

if they have no outcomes in common and so they can never occur together, P(A and B) = 0

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

the probability that one event happens given that another event is already known to have happened; P(A|B) = P (A and B) / P(B)

if the occurrence of one event does not change the probability that the other event will happen

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

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

a variable whose value is a numerical outcome of a random phenomenon

has a countable number of possible values

takes all values in an intervale of numbers and is measurable

𝝁𝒙 = 𝑬(𝒙) = ∑𝒙𝒊∙ 𝒑𝒊 = 𝒙𝟏 ∙ 𝒑𝒊 + 𝒙𝟐 ∙ 𝒑𝟐 + ⋯ + 𝒙𝒌 ∙ 𝒑𝒌

Binary - each observation is a success or failure

Independence - observations must be intendent, the result of one does not affect another

Number - procedures has a fixed number of trials (n)

Success - probability of success (p)

P (X = k) = n! / k! (n-k)! (p)^k (1-p) ^n-k

the probability distribution function and determines P(X=k)

a cumulative distribution function and determines P (X < or = k)

=np

Binary - each observation is either a success or failure

Independence - the observations must be independent, result of one does not affect another

Trials - variable of interest is the number of trials required to obtain the first success

Success - probability of success (p)

P(X=n) - (1-p)^n-1(p)

the probability distribution function and determines P(X=n)

a cumulative distribution function and determines P(X , or = n)

= 1/p