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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