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3.10.7 Calculate E(Y) for the following pdf's: (a) fr(y) = 3(1 - y)', Osys1 (b ) fr (y ) = 4 ye-2x, y >0 (3/4, OSys1 (C) fr (y) = 1/4, 2 sys3 (d) fr(y) = siny, 0sys #/2 10, elsewhere 3.10.8 Show that fr (y ) = 2, y21 is a valid pdf but that Y does not have a finite expected value. 3.10.9 Let the random variable Y have the uniform distribution over the interval [a, b] (recall Example 2.5.1). Find E(Y) using Definition 3.10.1. Also, deduce the value of E(Y), knowing that the ex- pected value is the center of gravity of fr()). 3.10.10 Show that the expected value associated with the exponential distribution, fr(y) = Ae Ay, y > 0, is 1/A, where A is a positive constant. questions 3.10.8 and 3.10.10 random variable chapter ( expected value)