A manufacturing company has developed a fuel efficient machine for cleaning carpet because it delivers carpet cleaner so rapidly. Of interest is a random variable Y, the amount in gallons per minute delivered. It is known that the density function is given by(a) Sketch the density function.(b) Give E(Y), E(Y2), andVar(Y).

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S1, 7s>Js 8, 10, fiy) fiy) = ssewhere.