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Expected Value of a Discrete Random Variable (E(X))
: X
i
= the
i
th outcome of the discrete random variable X;
P(X
i
) = probability of occurrence of the
i
th outcome of X; multiply for each X value and then sum for the mean.
Variance of Discrete Random Variable
(σ
2
)
: σ
2
= (XExpected Value)
2
(probability of X) sum all values of X
Standard Deviation (σ)
: take the square root of the Variance
Covariance (σ
xy
)
: (XExpected Value of X)(YExpected Value of Y)(probability of XY) sum all values of XY;
positive covariance=positive relationship; negative covariance=negative relationship;
Variance of the Sum of
Two Random Variables
: σ
2
X+Y
=
σ
2
X
+σ
2
Y
+2σ
2
XY
BINOMIAL DISTRIBUTION
Four Essential Properties
: (1) sample consists of a fixed number of observations, n. (2) each observation is
classified into one of two mutually exclusive and collectively exhaustive categories, usually called success and
failure. (3) probability of an observation being classified as success,
p
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 Fall '07
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