A dealer's profit, in units of $5000, on a new automobile is given by Y = X2, where X is a random variable having the density function(a.) Find the probability density function of the random variable Y.(b) Using the density function of Y, find the probability that the profit will be less than S500 on the next new automobile sold by thisdealership.

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S2(1 - r), 0< x< 1, S(x) = to, 10, elsewhere.