Applied Stats, Class 3: Transformations of Random Variables, Bivariate RVs, Simulation (Spreadsheet)

Applied Statistics, Class 3. If Z is N(0,1) (standard normal), then Z^2 is chi-square with 1 degree of freedom. If U=F(X), then U is uniform on the interval (0,1) (where F is the CDF of X assumed to be strictly monotone increasing). Bivariate Random Variables: joint distributions, marginal distributions, conditional distributions (discrete and continuous). Introduction to probability simulation on a spreadsheet (with =RANDBETWEEN and =RAND()).

#probability #transformation #simulation

Links and resources
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(0:00) Class plan, including spreadsheet simulation
(0:49) If Z is N(0,1) (standard normal), what is the distribution of Z^2? It turns out to be chi square with 1 degree of freedom.
(23:55) U=F(X) is uniform on (0,1) when F is a strictly monotone increasing CDF for a continuous random variable X
(38:50) Bivariate random variables (joint distributions, marginal distributions, conditional distributions, means, covariance, and independence; in both the discrete and continuous cases)
(53:44) Simulation of a binomial random variable in a spreadsheet (with =RANDBETWEEN)
(1:05:03) Simulation of an exponential distribution in a spreadsheet (with =RAND() and the inverse function of the CDF)

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