Chapter 7. Section 7.2 – Means and Variances of Random Variables. Means and Variances of Random Variables. Probability is the mathematical language that describes the long-run regular behavior of random phenomena.
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Section 7.2 – Means and Variances of Random Variables
Payoff X: $0 $500
Probability: 0.999 0.001
Value of X: x1 , x2 ,x3 , …. xk
probability: p1 , p2 , p3 , ….. pk
= x1 p1 + x2 p2+ …….xkpk=
Suppose that Xis a discrete random variable whose probability distribution is
Value: x1x2x3 …
Probability: p1p2p3 …
and that µXis the mean of X. The variance of X is
The standard deviation σx of X is the square root of the variance.
Units sold: 1000 3000 500010,000
Probability: 0.1 0.3 0.4 0.2