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c4_3ExpValCRVs - 4.3 Expected Values For Continuous Random...

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4.3 Expected Values For Continuous Random Variables (CRV) Definition: The expected value for a continuous random variable Y is E (Y) where dy y yf Y E ) ( ) ( Theorem: Let g (y) be a function of c.r.v. Y then dy y f y g y g E ) ( ) ( )) ( ( Theorems: If c is any constant and Y a c.r.v. then 1. E(c) = c 2. E[c g(y)] = c E( g(y) ) 3. E[g 1 (y) + g 2 (y) +…..g k (y)] = E[g 1 (y)] +……+E[g k (y)] Example: If Y has pdf #4.15 Pg. 164 f(y) = (3/2) y 2 + y , 0 < y < 1 0 , other wise
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