Unformatted text preview: F ( y ) = P ( X ≤ y ). In the case of discrete ran-dom variables, this is not particularly useful, although it does serve to unify discrete and continuous random variables. In the continuous case, the fun-damental theorem of calculus tells us, provided f satisﬁes some conditions, that f ( y ) = F ( y ) . By analogy with the discrete case, we deﬁne the expectation by E X = Z ∞-∞ xf ( x ) dx. In the example above, E X = Z ∞ 1 x 2 x 3 dx = 2 Z ∞ 1 x-2 dx = 2 . 26...
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- Spring '10
- probability density function, dx