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Unformatted text preview: alues based on chance.
In the case of the coin, we know X has two outcomes, x1 =“heads” and x2 =“tails”. If the
coin is fair, we know that it will be heads half the time and be tails half the time. In other
words, if we denote the outcome of the coin ﬂip by X , we know that
x1
X =
x
2
with probability 1
2 with probability 1 .
2 And the above “distribution” of the probabilities over outcomes is the distribution of the
random variable X .
The likelihood that the random event will be a particular outcome (“heads” and “tails”) is
called the density of the distribution.
In reality, there are a lot of uncertain events. Most of them have very complicated outcomes,
much more so than “heads” and “tails”. Therefore it is very useful to understand random
27 EC 271 Applied Statistical Methods: Lecture Notes (Leshui He) 2014 distributions with “continuous”, rather than “discrete”, o...
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 Fall '13
 Alexandru
 Probability

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