BIOL 335 Lecture 2: ch2_v1

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20 Oct 2017
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Essentially, all models are wrong, but some are useful. Statistics stochastic models exploratory data analysis descriptive statistics tabular & graphical data summaries. Statistical inference ( tted model) (frequentist, bayesian, non-parametric (e. g. least squares)) Statistics random variable, xt observation, xt discrete-time stochastic process, {xt} joint distribution function of {xt} (model) s n o i t a c i l p p. A historical time series, {xt}t=1,,n empirical distribution function of {xt} Expected value or mean ( rst moment) of x : e(x ) :=r x df (x) Interpretation: weighted average of all possible values of x. Linearity: e(ax + by ) = a e(x ) + b e(y ) (a constants) Variance (second moment) of x : var (x ) := e[(x e(x ))2] Interpretation: measure of how spread out the distribution of x is in relation to its mean. Square root of the variance is known as the standard deviation.

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