QSCI 381 Module 4: Probability Distributions

probability distribution

mathematical function that enables us to calculate the probabilities of observations when given population parameters and/or information about the observation process

probability distribution observations/ possible observations

the result of a random trial

probability distribution outcome

random variable, X

x

a specific outcome or particular value of random variable X

P(X = x)

the probability that the measured variable X took a specific value x

discrete random variable

a random variable with a finite or countable number of possible outcomes, and outcomes must have integer values

continuous random variables

uncountable number of possible outcomes, and outcomes can take any possible numeric value

discrete probability distribution

lists each possible value a random variable can take, together with the probability of it occurring

discrete probability distribution conditions

• probability of each possible outcome between 0 and 1

• sum of probabilities across all outcomes equals 1

expected value E(X)

long-term mean of measurements based on its probability distribution

deviation

difference of an observation from the mean