Screenshot 2018-09-30 at 00.25.28.png - Random Variables Generally the object of an investigators interest is not necessarily the action in the sample

Screenshot 2018-09-30 at 00.25.28.png - Random Variables...

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Unformatted text preview: Random Variables Generally the object of an investigators interest is not necessarily the action in the sample space but rather some function of it. Technically a real valued function or mapping whose domain is the sample space is called a “Random Variable”, it is these that are usually the object of an investigators attention. If the mapping is onto a finite (or countably infinite) set of points on the real line, the random variable is said to be discrete. Otherwise, if the mapping is onto an uncountably infinite set of points, the random variable is continuous. This distinction is a nuisance because the nature of thing which describes the probabalistic behaviour of the random variable, called a Prob ability Density Function (denoted here as f(x) and referred to as a p.d.f.), will differ according to whether the variable is discrete or continuous. In the case of a discrete random variable X, with typical outcome x1- , (it shall be assumed for convenience that the xi’s are ordered with i from smallest to largest), the probability density function f(x].) is simply the sum of the probabilities of outcomes in the sample space which result in the random variable taking on the value xi. Basically the p.d.f. for a Discrete Random Variable obeys 2 rules: In the discrete case f(xi) = P(X=x]-), in the continuous case it is not possible to interpret the 11" l‘ ' 1 1 ‘ ‘7 ‘1 l‘ 1" ‘ f‘ '1 . f‘ ...
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  • Spring '14
  • Schmid
  • Economics, Probability distribution, Probability theory, 1 L

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