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Unformatted text preview: X , F X ( x ). (c) The median of a distribution of a continuous random variable X (denoted by m ) is the value that half the area under the density function is to the left of it and half the area is to the right. In other words, the median m satisﬁes: P ( X ≤ m ) = . 5, which means that the random variable X is as likely to get values below m as it is to get values above m . Find the median of the distribution above. 1 8. Page 173, problem 4.30 (a) and (b) only 9. Page 173, problem 4.31 10. A family of pdf’s that has been used to approximate the distribution of income, city popula-tion size, and size of ﬁrms is the Pareto family. The family has two parameters, k and θ , and the pdf is: f X ( x ) = kθ k x k +1 x ≥ θ otherwise If k > 1, compute E ( X ) and explain why you need the fact that k > 1. 2...
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- Summer '09
- Probability theory, probability density function, density function, legitimate density function