Probability Mass Function
A probability mass function (PMF) has the form: P(X = x) = some expression (usually containing x) that produces a probability of observing x = P(x)
1. P(x) is between 0 and 1 (inclusive) for each x
2. ∑P(x) = 1
Mean of Discrete Random Variables
The mean of a discrete random variable represents the average value of the random variable if you were to observe this variable over an indefinite period of
time. The mean of a discrete random variable is written as
µ
µ = ∑xP(x)
Variance of Discrete Random Variables
The variance of a discrete random variable, X, is a parameter describing the variation of the corresponding population. The symbol used is
σ
2
σ
2
= ∑(x  µ)
2
• P(x)
σ
2
= ∑x
2
P(x)  µ
2
Using Binomial Table A.1 to Determine Probabilities
The binomial PMFs have been tabulated in Table A.1 for various values of n and p. If n = 4 and p = 0.3 and you wish to find the P(2) locate n = 4 and x = 2.
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 Spring '08
 ONE
 Probability theory, nCk

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