Constructing a probability distribution for random variableValid discrete probability distribution examplesProbability with discrete random variable exampleMean (expected value) of a discrete random variableVariance and standard deviation of a discrete random variableMean and standard deviation of a discrete random variable
AP Stats: VAR (BI), VAR‑5 (EU), VAR‑5.E (LO), VAR‑5.E.1 (EK), VAR‑5.E.2 (EK), VAR‑5.E.3 (EK)
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 probability exampleGeneralizing k scores in n attemptsFree throw binomial probability distributionGraphing basketball binomial distributionBinompdf and binomcdf functionsBinomial probability (basic)
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
A random variable is some outcome from a chance process, like how many heads will occur in a series of 20 flips (a discrete random variable), or how many seconds it took someone to read this sentence (a continuous random variable). We calculate probabilities of random variables, calculate expected value, and look what happens when we transform and combine random variables.
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