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**Yan** Suppose that P, the price of a certain commodity (in dollars), and S, its total sales (in 10,000 units), are random variables whose joint probability distribution can be approximated closely with the joint probability density

f(p,s)=5pe^(-ps) for 0.2<p<0.4, s>0 and 0 elsewhere

Find the probabilities that

(a) the price will be less than 30 cents and sales will exceed 20,000 units;

(b) the price will between 25 cents and 30 cents and sales will be less than 10,000 units;

(c) the marginal density of P;

(d) the conditional density of S given P=p;

(e) the probability that sales will be less than 30,000 units when p=25 cents.