Common Probability Distributions Flashcards
All possible outcomes of an experiment, along with their associated probabilities
Probability distribution
A random variable with positive probabilities associated with a finite number of outcomes
Discrete random variable
A random variable with positive probabilities associated with a range of outcomes values
Continuous random variable
A distribution where there a n discrete, equally likely outcomes
Discrete uniform distribution
A probability distribution for a binomial (discrete) random variable that has two possible outcomes
Binomial distribution
Formula for probability of success in binomial distribution
= NCr x Px x (1-p)^n-x
A distribution where the probability of X occurring in a possible range of is the length of the range relative to the total of all possible values
Continuous uniform distribution
= (x2 - x1) / (b - a)
Confidence Interval Formula
= x-bar - reliability factor x standard error
Common confidence intervals (i.e. 90, 95, 99)
90% = 1.65 95% = 1.96 99% = 2.58
Critical Value Formula
= x - μ / σ
Safety First Ration
= E(Rp) - RT / σp
The probability that a portfolio’s value/return will fall below a specific value over a given period of time
Shortfall risk
Lognormal distribution
Used to model asset prices, bounded by zero, if x is normally distributed E^x follows a lognormal distribution
A simulation using randomly generated values for risk factors, based on their assumed distributions to produce a distribution of possible security values
Monte Carlo
Monte Carlo limitations
Fairly complex and only as good as the assumptions used
