With reference to Exercise 3.101, 

In exercise

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

Find 

(a) The marginal density of P; 

(b) The conditional density of S given P = p; 

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

fp.s)-5pe-or 0.20p040,s 0 rp,s) =to elsewhere