DIFFERENT DISTRIBUTIONS Random Variables - Discrete Random Variables => there’s a finite number, e.g. numbers of people. - Continuous Random Variables => there’s an infinite number, e.g. heights. Functions - Probability Function…
- Probability Density Function => is the term used for a function for a Continuous Random Variable; used to determine probability that it will fall in a range, e.g. p (1.35m < height < 1.45m) = 0.3 - Cumulative Density Function => gives the probability that a random variable will be less than or equal to a specific value, in graphical terms it is the area under the graph.
- Discrete Uniform Distribution => in a distribution which is discrete there are n outcomes (as it is based on a discrete random variable). Hence if it is a discrete uniform distribution then there are n equally likely outcomes. - Binominal Distribution => if X is a discrete random variable with the binomial distribution (each experiment has a yes/no outcome) and probability p of success, q = 1-p of failure and n trials…
- Tracking Error = Total Portfolio Return – Return on Benchmark
- Continuous Uniform Distribution => for a distribution of a continuous random variable that runs from a lower limit, a, to an upper limit b…
- Normal Distribution => the normal distribution is a continuous probability distribution with parameters, μ, the mean and σ2, the variance. It is written as…
The rules of the normal distribution include… - Confidence Internal => X is an interval estimate of a population parameter and is defined as…
…where
- Standard Normal Distribution => Z is a special case of the normal distribution function where the mean μ = 0 and the variance σ2 = 1, so that… Remember… o If Z < test statistic => fail to reject the null hypothesis, Ho. o If Z > test statistic => reject the null hypothesis, Ho.
And…