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# Elem Stats ch 5

### A Brief Version: Elementary Statistics Ch 5

Random Variable A variable whose values are determined by chance.
Discrete Probability Distribution Consists of values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation.
What are the requirements for a probability distribution? The sum of the probabilities of all the events in the sample space must equal 1. The probability of each event in the sample space must be between or equal to 0 and 1.
Mean of Probability Distribution (mu)= The sum of the products X and P(X).
The Expected Value E(X) of a discrete random variable of a probability distribution is: The theoretical average of the variable.
Binomial Distribution The outcomes of a binomial experiment and the corresponding probabilities of these outcomes.
Binomial Experiment must satisfy what requirements? There must be a fixed number of trials. Each trial can involve only 2 outcomes or outcomes that can be reduced to 2. The outcomes of each trial must be independent of one another. The probability of a success must remain the same for each trial.
P(S) = The symbol for the probability of success. P(S)= p
P(F) = The symbol for the probability of failure. P(F)= 1 - p = q
p = The numerical probability of a success. P(S)= p
q = The numerical probability of a failure. P(F)= 1 - p = q
n = The number of trails.
X = The number of successes in n trials.
! = Factorial
Mean of the Binomial Distribution (mu) = n*p
Variance of the Binomial Distribution (sigma squared) = n*p*q
Standard Deviation (sigma) = square root of (n*p*q)
Created by: dengler