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4. Let Xdenote the price paid for a barrel of crude oil by the initial carrier, and Y den ote the price paid by the refinery purchasing the oil. The joint PDF is given by: 20 x y 40 otherwise fx,y(x,y) = 150 0 a) (4 points) Find E[X], E[Y]. b) (4 points) Let W Y-X, Find F,(w) andhr(w). c) (2 points) Find the expected value of W.
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150 504 150 C40-* 150 150 1500 150 1 50 9-20 150 ο x2-98 140 3 40%-X2 150 1 50 20 64000 /20 3 1S0 - 6400 O24000- 800 150 3 [31 82800 150 - 32800328 9 1o 20 20 1S0 20 20 401 [wtx-2014ス 1SO 5o 20 1 โ404 50 300-800-[2014 200-400 | 20ω S0 - 20 w 10 20 S480 20 302 J26 . 4 T 1600-400 3 0 2. 30 - 480060 6 0

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