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Unformatted text preview: V X b a ( ) =2 12 4 Example: Mean & Variance of a function of a random variable The lifetime of a battery is exponentially distributed with mean 2; i.e, f x e x x ( ) . . . = ≥5 5 E(X)=2 and V(X)=4 • The cost to operate the battery is a function of X: C=5+3x. Find the mean and variance of the cost. • The cost to operate the battery is D=3x 2 . Find the mean of the cost. 5 Percentiles The p th percentile of the r.v. X is the number such that a p percent of the distribution is less than that number The life of a component has the exponential distribution E(X)=1; i.e., f x e x x ( ) = ≥Find the 50 th percentile (the median) = .69 Find 99 th percentile = 4.6 50 percentile: Find m such that e dx e e m m x m m m= ⇔= ⇔ = ⇔= ⇔ = ∫ . . . ln. . 5 1 5 5 5 1 69 Note: for exponential mean ≠ median 6 7...
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 Spring '09
 NA
 Normal Distribution, Probability theory, probability density function, continuous random variable

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