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DR. DOUGLAS H. JONES
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Let S be a discrete sample space with the set of elementary events
denoted by E = {e
i
, i = 1, 2, 3…}. A random variable is a function Y(e
i
)
that assigns a real value to each elementary event, e
i
. The random
variable is denoted by Y.
The set of all possible values of Y is the set {y
i
= Y(e
i
), i = 1, 2, 3…}. The
set of all possible values of Y is a finite or countably infinite set, and Y is
said to be a discrete random variable.
Let y be the set of values of Y. The subset of all elementary events that
are assigned the y, is the compound event {e
i
: Y(e
i
) = y}. Usually the
probabilities of all the elementary events are known, therefore the
probability of this compound event can be readily computed by summing
over all the elementary events.
Toss a coin twice. Let Y denote the number of heads.
Denote (Tail, Tail) to be the elementary event that the first toss is tail and
the second toss is tail. Denote the other elementary events accordingly.
Compound Event
Elementary Events
(Y=0)
(Tail, Tail)
(Y=1)
(Tail, Head), (Head, Tail)
(Y=2)
(Head, Head)
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View Full DocumentDR. DOUGLAS H. JONES
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Let Y be a discrete random variable. A probability mass function is f(y) =
P{e
i
: Y(e
i
) = y}. It is a function with values between 0 and 1 and whose
sum is 1 over all values of y.
Toss a balanced coin once. Let Y be the number of heads that occurs.
Find the probability mass function of Y.
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 Fall '08
 Tucker,A

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