Common Probability Distributions Flashcards
Probability Distribution
- describes the probabilities of all possible outcomes for a random variable
- all probabilities must sum to 1
Discrete random variable
a variable where the number of possible outcomes can be counted, measured, and given a positive probability
p (x)
probability function
A probability functions two key properties
- Each individual prob must be between 1 & 0
2. All probabilities must sum to 1
Continuous Randndom Variable
possible outcomes are infinate
p (x) is read as…
“The probability that random variable X=x”
Cumulative distribution function (cdf)
- defines that prob that random variable X, is equal to or less than the specific value of x.
- Represents the summ of probs for outcomes up to and including that specific outcome
Discrete uniform random variable
probabilities for all possible outcomes for a discrete random variable are equal
Binomial Random Variable
Defined as the number or “successes” in a given number of trials, where the outcome is either a failure or a success
Binomial random variable with 1 trial
Bernoulli Trial
What does “p” denote with a binomial random variable?
“p” in a binomial distribution stands for probability of success, NOT p(x)
Expected Value of a Binomial random variable equation
E(X)= np
-where n= number of trials and p= prob of success
Variance of Binomial random variable equation
Variance of X = np(1-p)
One important application of a Binomial Stock Price Model
pricing options, be shortening the length of periods and increasing the amount of periods
Tracking Error
The difference between the total return on a portfolio and the total return on the benchmark against which its performance is measured
Other name for Tracking Error
Tracking Risk
Continuous Uniform Distribution
defined over a range that spans between a lower limit (a) and an upper limit (b), which serve as parameters
90% Confidence Interval number
1.65
95% Confidence Interval number
1.96
99% Confidence Interval Number
2.58
Lognormal Distribution
similar to the normal distribution, but is bound from going below zero, making it more applicable
z score equation
(X-mean)/ STDV
A z-score of 1 means that
the observation is 1 STDV above the mean
Roys Safety First Equation
(E(Rp) - RL) / STDV
Essentially the Sharpe equation but with min threshold level instead of rFr
