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Let x denote the prison sentence in years for people

Let X denote the prison sentence, in years, for people convicted of auto theft in a particular state in Canada.

Suppose that the pdf of X is given by f(x) = ax^2 , for 0 < x < 2.

(a) What is the number a that makes f(x) be an appropriate pdf?

(b) What is the expected prison sentence E(X)?

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