Reading 9: Probability Concepts Flashcards
LOS 9.A- Define a random variable, an outcome, an event, mutually exclusive events and exhaustive events.
Random Variable- a random variable is a variable that is given a random name like “x” to represent a wanted number.
Outcome- the outcome is the observed value of a random variable. ex: x=5
Event- is a single outcome or a set of outcomes
Mutually Exclusive Events- 2 events can’t occur at the same time. You can not flip a coin and get heads and tails.
Exhaustive Events- this includes all possible outcomes for an event.
LOS 9.B- State the “2 defining properties of a probability” and then we will go into depth about the 3 different types of probability.
Properties of a probability:
- ) All probabilities will be less than 1
- ) Sum of all probability of outcomes of an event is equal to 1.
LOS 9.B- What are the 3 different types of probabilities?
Empirical Probabilities- which are based on past data.
Priori probabilities- probabilities that are made after an inspection process and formal reasoning.
Subjective Probabilities- use of personal judgement to give rough probabilities
Objective Probabilities- use of empirical and priori probabilities are considered objective.
LOS 9.C: State the probability of an event in terms of odds for and odds against the event.
ODDS & PROBABILITIES are NOT THE SAME EVENT.
ODD= (Probability of an event)/ (1- Probability of an event)
Probability= Probability of an event
LOS 9.D: Distinguish between unconditional and conditional probabilities
Unconditional Probability- refers to the probability of an event regardless of past or future occurrences of other events
Conditional Probability- 1 Event affects the outcome of another event.
LOS 9.E: Explain the multiplication rule, addition rule, and total probability rules.
Multiplication Rule of Probability-
States that P(AB)= P(A/B)* P(B)
Addition Rule of Probability-
P(A or B) = p(a) +p(b) -p(ab)
Total Probability Rule-
P(A)= P(A/B1)(B1) + P(A/B2)(B2)
***Total probability rule is used when the conditional probability is multiplied by second value till all conditional probabilities are taken into account. Allows you to get to P(A)
LOS 9.F: Calculate and Interpret:
1.) Joint probability of 2 events (MULTIPLICATION RULE)
The joint probability that 2 events will occur is:
P(AB)= P(A/B)*P(B)
LOS 9.F: Calculate and interpret the probability that @ least 1 of 2 events will occur. (ADDITION RULE)
@ Least 1 of 2 events will occur includes:
P(A or B)= P(A) +P(B) - P(AB)
LOS 9.F: Calculate and interpret the joint probability of any number of events occurring:
Independent:
*P(AB) = P(A) * P(B)
Dependent:
P(AB) = P(A/B) * P(B)
LOS 9.G: Distinguish between dependent and independent events
1.) Independent Events- refers to an event where any one event has no relation to another occurrence of a probability.
P(A/B) = P(A)
2.) Dependent Events- conditional probabilities; think about conditional probabilities
LOS 9.H: Calculate and interpret an unconditional probability using total probability rules
Total Probability Rule= using conditional probabilities to solve an unconditional probability
P(A) = P(A/B1)P(B1) + P(A/B2)P(B2) + P(A/B3)* P(B3)…….
LOS 9.H: How do you calculate the expected value of a data set.
E(x) = [p(x1)](x1) + [p(x2)](x2) + [p(x3)]*(x3)………..
Ex: used to find expected EPS**[E (EPS)]**
LOS 9.H: How do you calculate the expected value of a data set. Explain how to solve the VARIANCE OF EPS.
VARIANCE EPS = SUM [ (ACTUAL#- E(X))^2 ]
SD EPS = (VARIANCE EPS)^1/2
LOS 9.K: Calculate & Interpret Covariance & Correlation.
Calculate the covariance:
How to find covariance:
- ) Find the Expected values for each data set.
- ) Take those values and subtract from given values in the data set.
- ) Multiply the probability of an outcome occurring by the difference of E(x) + value.
- ) Multiply all of those values together.
“COV (A,B)= P(S)* (A-E(A))* (B-E(B))”
LOS 9.K: Calculate & Interpret Covariance & Correlation.
Calculate the correlation coefficient between 2 Variables:
Correlation Coefficient = Cov (A,B)/ (SD A) * (SD B)
How do you find a single SD for one variable?
- ) First find the variation. Which means you need to find the expected values.
- ) VARIATION (A) = SUM [(X-e(A))^2]
- ) SD(A) = (VARIATION)*(1/2)
