Probability Concepts Flashcards
“What is the probability of this event A?”
Example of…
Unconditional probability
What is the probability of A, given that B has occurred?
Example of…
Conditional probability
Definition of expected value?
The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable.
Expected value of ‘X’ notation…
E(X)
Expected variance equals…
the sum of probability weighted, squared deviations from the expected value.
Calculation of portfolio expected return…
Given a portfolio with n securities, the expected return on the portfolio is a weighted average of the returns on the component securities.
Definition of correlation…for variables Ri and Rj
Cov(Ri,Rj) / st.d(Ri)*st.d(Rj)
Correlation is equal to the covariance between the two variables divided by the cross product of their standard deviations.
Two random variables X and Y are independent if and only if…
P(X, Y) = P(X)P(Y)
Baye’s formula states that given a set of prior probabilities for an event of interest, if you recieve new information, the rule for updating your probability of the event is…
Probability of the new info given event
divided by…
Unconditional probability of the new information
all multiplied by…
Prior probability of event
What does a probability distribution specify?
It specifies the probabilities of the possible outcomes of a random variable.
What are the two basic types of random variables?
Discrete random variables
Continuous random variables
Discrete random variable
Can take on at most a countable number of possible values.
Rate of return is an example of what kind of variable?
Continuous random variable
What does the cumulative distribution function give us?
It gives us the probability that a random variable X is less than or equal to a particular value x, P(X<=x)
How does the cumulative distribution function relate to the probability function?
To find F(x), we sum up, or cumulate, values of the probability function for all outcomes less than or equal to x.
What is the simplest of all probability distributions?
Discrete uniform distribution
What is the building block of the binomial distribution?
the Bernoulli random variable
What is a Bernoulli trial?
A trial, or event that may repeat, that produces one of two outcomes.
n! is defined as
n(n-1)(n-2)…1
3!
(3)(3-1)(3-2) = (3)(2)(1) = 6
Binomial distributions are symmetric when…
When the probability of success on a trial is 0.50, bit is asymmetric or skewed otherwise.
A binomial distribution is completely described by two parameters, ____ and ____
n
p
Bayes:
Conditional probability of a hypothesis (H) given new evidence (E) depends on three things…
Conditional probability of E given H
The prior probability of the hypothesis H
The prior probability of the evidence E
What is ‘base rate fallacy’?
In behavioral finance?
Cognitive error whereby too little weight is placed on the base (original) rate of possibility.
In behavioral finance, it is the tendency for people to erroneously judge the likelihood of a situation by not taking into account all the relevant data and focusing more heavily on new information without acknowledging how the new information impacts the original assumptions.
