# Random variables

## Discrete random variables

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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
Practice
Constructing probability distributionsGet 3 of 4 questions to level up!
Probability modelsGet 5 of 7 questions to level up!
Probability with discrete random variablesGet 3 of 4 questions to level up!
Expected valueGet 5 of 7 questions to level up!
Standard deviation of a discrete random variableGet 3 of 4 questions to level up!

## Continuous random variables

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Probability density functionsProbabilities from density curves
Practice
Probability in density curvesGet 3 of 4 questions to level up!
Probability in normal density curvesGet 3 of 4 questions to level up!

## Transforming random variables

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Impact of transforming (scaling and shifting) random variablesExample: Transforming a discrete random variable
Practice
Transforming random variablesGet 3 of 4 questions to level up!

## Combining random variables

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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
Practice
Combining random variablesGet 3 of 4 questions to level up!
Combining normal random variablesGet 3 of 4 questions to level up!

## Binomial random variables

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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)
Practice
Identifying binomial variablesGet 3 of 4 questions to level up!
Binomial probability formulaGet 3 of 4 questions to level up!
Calculating binomial probabilityGet 3 of 4 questions to level up!

## Binomial mean and standard deviation formulas

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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
Practice

## Geometric random variables

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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
Practice
Binomial vs. geometric random variablesGet 3 of 4 questions to level up!
Geometric probabilityGet 3 of 4 questions to level up!
Cumulative geometric probabilityGet 3 of 4 questions to level up!

## More on expected value

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Term life insurance and death probabilityGetting data from expected valueExpected profit from lottery ticketExpected value while fishingComparing insurance with expected valueLaw of large numbers
Practice
Expected value with empirical probabilitiesGet 3 of 4 questions to level up!
Expected value with calculated probabilitiesGet 3 of 4 questions to level up!
Making decisions with expected valuesGet 3 of 4 questions to level up!

## Poisson distribution

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Poisson process 1Poisson process 2