random variable - mapping from event to probability

random variable - mapping from event to probability - The...

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rnorm - generate normal random variables rt - generate random t distribution rpois - generate random poisson numbers fun-name <- function(x) { y=x^2 return(y) } ----- random variable - mapping from event to probability sigma(x bar) = sigma/root(n) margin of error - x(bar) +- z(alpha/2) * sigma(x bar) Two ways of hypothesis testing Test statistics P-value The probability that you can observe the sample mean If Ho is true, how likely is it that I am going to observe my data? multiply the p value by two for two tailed distributions -------- The main difficulty is that the variability of the graph changes over time The range changes The statistical measure is the variance and the variance is much different based on the range covariance of x and y is cov(x,y) cov(x,y) = E(xy)-E(x)E(y) E(xy) is the expected value of x*y

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Unformatted text preview: The higher the cov, the more confident we are about the future values …. just for linear autocorrelation - correlation defined for variables over different time points autocovariance (variance between x1 and x5 is autocovariance with 4 steps [over time]) auto - just measured over time correlation standardizes the covariance by making it on a scale from -1 to 1 ACF = autocorrelation function difference btwn xT and Xt-1 is very small, second line is xt and x(t-2) HOW TO CALCULATE ACF BY HAND Mean Absolute Error: MAE = mean(abs(Et)) [the average of the errors] Root mean square error: RMSE = root(mean(Et(squared))) Mean absolute percentage error: MAPE = mean(abs(pt)) where pt = 100Et / yt Least square estimate: sigma[yi - B0 -B1(xi)](squared]...
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