Chapter 4:

Question 1

the sum of the probabilities must add up to what?

Answer 1

100% every outcome has an individual probability of between 0% and 100%

Question 2

what does 0% indicate

Answer 2

impossible

Question 3

what does 100% indicate

Answer 3

guarantee

Question 4

outcomes need to be what?

Answer 4

1. exhaustive 2. mutually exclusive

Question 5

what does exhaustive mean

Answer 5

all possible outcomes are covered - there are no other possible outcomes

Question 6

what does mutually exclusive mean

Answer 6

only one of the outcomes can occur at a time - only one of the outcomes can occur each time the experiment is run

Question 7

what are the approaches for assigning probabilities

Answer 7

1. Priori classical 2. empirical classical probability 3. subjective

Question 8

define Priori classical probability approach

Answer 8

if each outcomes has an equal chance of occurring - count the number of possible outcomes and divide by 100% total into that many equal pieces (4 categories, assign each with a 35% chance for example)

Question 9

define the empirical classical probability approach

Answer 9

what has happened in the past is a good predictor of what happens in the future - observing weathers form the past as being a good predictor for the future

Question 10

what is conditional probability

Answer 10

the likelihood of one event or outcome if you know that another event or coutcomes has happened

• use a Ven diagram
• ex. if you know that it is raining, what is the probability that the temperature will be greater than 10C

P(A|B) = 1 or 3 rainy days will have temp > 10 C

P(A and B) so, P(B|A) = 1/3 = 33%

P(B)

= .10/.15 = 66.7%

Question 11

define the subjective probability approach

Answer 11

make an educated guess based on research and judgement - use when there is no historical data to look at and if we believe they are not equal split

Question 12

what are the probability theories and rules

Answer 12

1. joint 2. marginal 3. conditional probability

Question 13

define joint probability

Answer 13

a probability that reflects the outcome of two different events

• ex. what is the probability tha tit will be raining AND that the temperature will be greater than 10C

A = rain P(A) = 30%

B = temp is greater than 10 C P(B) = 15%

Question 14

what is marginal probability

Answer 14

uncondintional probabiltiy

• use a joint probability table
• individual probabilites of A and B taken seperately
• use a joint probability table and
• adding up probabilites at the margins
• convert the Ven diagarms into this table

Question 15

How do you calcluate Marginal Probability

Answer 15

well we know it must add up to one for the marginal probabilities

so we then can figure out the remainng numbers

Question 16

what do you also need to figure out with regards to marginal probability

Answer 16

whether it is indepndint or dependent

Question 17

if two outcomes are independent then

Answer 17

the probability of one happening will be the same regardless of whether the other one happens

indepnedint if P(A) = P(A|B) or if P (B) = P(B|A)

• independent if P(Rain) = P(Rain|Temp >10)

but 30% is no equal to 67%, so these are dependent

Question 18

What is probability distribuiton

Answer 18

all possible outcomes form an experiment and the probabilites associated with each outcome

• the probability of each outcome is between 0 and 1
• the sum of the probabilites of all outcomes equal 1
• can be a table, a graph, or a forumula
• lists the probabilities of different outcomes

Question 19

what is discrete probability distirbution

Answer 19

the probability distirbuiton of discrete random variable

Question 20

What is a discrete Random vairable?

Answer 20

a variable that only can have a limited number of values within a given range of values

• the number o fpossible vlaues can be counted
• dollar values, numbre of times something happens, number of objects etc

Question 21

what are examples of discrete ramdon variables

Answer 21

dollar values, number of times somehting happnes, number of objects etc

Question 22

what is a continuous random variable

Answer 22

a variable that can assume an infinite number of values

• the number of possible vlaues cannot be counted

Ft, time, temperature etc

Question 23

What is expected value

Answer 23

of discrete random variables = it’s mean

• sum of each variable times its probability

Question 24

what is variance?

Answer 24

• expected value of x squared

add more confusing

Question 25

Example 3-2

An auditor examines three invoices chosen at random from all the invoices issued during the month

a) Assuming that 10% of this very large population of invoices are in error, create a probability distribution of the random variable, x, defined as the number of incorrect invoices in the sample of 3 invoices.

B)What is the probability the auditor will select two incorrect invoices out of the 3?

c) Calculate the mean (Expected value) of incorrect invoices and its variance and standard deviation

Answer 25

Determine the probability of distribution

step 1: begin by determing all the possible vlaues of x

x = the number of invoices chosen tha thave errors

possible values of x = 0,1,2,3

x = 1 can happen 3 ways:

1. error, no error, no error
2. no error, error, no error
3. no error, no error, error

what are hte possible outcomes:?

number of outcomes for 1st invoic x number of outcomes for 2nd invoice x number of outcomes for 3rd invoice 2 x 2 x 2 = 8 outcomes

Then calculate

Question 26

what are the multiplication rules

Answer 26

if two events are independent, the probability of both events occurring is:

P(Aand B) = P(A) x P(B)

if two events are not independent, the probability of both events occurring is:

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

Question 27

How do you calcluate the Variance and Standard deviation?

Answer 27

Variance

• expected value of x squared - the mean squared

expected value is calcualted by

• square each value of x multplied by the probability of x

then add them up

• standard deviation: is the square

Question 28

What is binomial Distribution

Answer 28

Bi means 2

• discrete probabiliity distribution when there are only two possible vlaues of x

(yes/no, heads/tails, on/off)

Question 29

what is Poission Distribution?

Answer 29

discrete probability distribution used to determine the number of times something happens in a given period of time

ex. number of people joining a line, number of fish swimming upstream

Question 30

add more notes from my little note book

Answer 30

start from begining of chapter 4 in my little note book

also need examples problems from my typed notes along with binomial and possion