ETC2410 Lecture 2: Review of Statistical Concepts
11 Nov 2018
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Random variables and their probability distributions: random variable - assigns a numerical outcome to an event e. g. rolling a die, starting wage offer to a graduate, discrete random variable - takes on a finite number of values, e. g. If we assume that var (u|x(cid:895) = 2, then we have a complete (cid:858)classical linear(cid:859) model. Independence: random variables x1, x2, , xn are independent random variables iff their joint pdf is the product of the individual pdfs for any (x1, x2, , xn) Features of probability distributions: expected value / mean - weighted average of all possible values of x, de(cid:374)oted either e(cid:894)x(cid:895) or , long-run average if we observe x many, many times. Var(ax + by) = a2 var(x) + b2 var(y) + 2ab cov(x,y) Standard deviation - positive square root of the variance: called the volatility in x, advantage: has the same units as x. Standardised random variable - has a mean of 0 and variance of 1.
