Quant - Probability Trees Flashcards
How is the expected value of a random variable calculated?
The expected value of a random variable is a probability-weighted average of the possible outcomes of the random variable.
For a random variable X, the expected value of X is denoted E(X).
What is the “variance” of a random variable?
The variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value E(X): σ2(X) = E{[X − E(X)]2}, where σ2(X) stands for the variance of X.
What are the units of “standard deviation”?
The same as of the dataset.
What does a probability tree illustrate?
A probability tree is a means of illustrating the results of two or more independent events.
What is a “conditional probability”?
the probability of an event given (conditioned on) another event is a conditional probability.
How do you calculate the “conditional expected value”?
Conditional expected value is E(X | S) = P(X1 | S)X1 + P(X2 | S)X2 + … + P(Xn | S)Xn and has an associated conditional variance and conditional standard deviation.
With respect to investing, what is the typical application of Bayes’ forumla?
Bayes’ formula is a method used to update probabilities based on new information.
What is the “investment version” of Bayes’ formula?
Updated probability of event given the new information =
[
(Probability of the new information given event)
/
(Unconditional probability of the new information)
] × Prior probability of event.
What does it mean if the variance of an event is zero?
If variance is 0, there is no dispersion or risk. The outcome is certain, and the quantity X is not random at all.
How do you calculate the variance of a random variable?
the probability-weighted average of squared deviations from the random variable’s expected value
How do you calculate the standard deviation of a random variable?
take the square root of the variance.
What is “conditional variance”?
The variance of one variable, given the outcome of another.
What are “prior probabilities”?
Probabilities reflecting beliefs prior to the arrival of new information.
What are “posterior probabilities”?
An updated probability that reflects or comes after new information.
