Random variablesDiscrete and continuous random variablesConstructing a probability distribution for random variableProbability models example: frozen yogurtValid discrete probability distribution examplesProbability with discrete random variable exampleMean (expected value) of a discrete random variableExpected value (basic)Variance and standard deviation of a discrete random variable
Mean of sum and difference of random variablesVariance of sum and difference of random variablesIntuition for why independence matters for variance of sumDeriving the variance of the difference of random variablesCombining random variablesExample: Analyzing distribution of sum of two normally distributed random variablesExample: Analyzing the difference in distributionsCombining normal random variables
Binomial variablesRecognizing binomial variables10% Rule of assuming "independence" between trialsBinomial distributionVisualizing a binomial distributionBinomial probability exampleGeneralizing k scores in n attemptsFree throw binomial probability distributionGraphing basketball binomial distributionBinompdf and binomcdf functionsBinomial probability (basic)
Mean and variance of Bernoulli distribution exampleBernoulli distribution mean and variance formulasExpected value of a binomial variableVariance of a binomial variableFinding the mean and standard deviation of a binomial random variable
Geometric random variables introductionProbability for a geometric random variableCumulative geometric probability (greater than a value)Cumulative geometric probability (less than a value)TI-84 geometpdf and geometcdf functionsProof of expected value of geometric random variable
Random variables can be any outcomes from some chance process, like how many heads will occur in a series of 20 flips. We calculate probabilities of random variables and calculate expected value for different types of random variables.