The random variable x represents the depth of rainfall in June, July, and August in Housto...

The random variable x represents the depth of rainfall in June, July, and August in Houston. The whole PDF is symmetric and is shaped as an isosceles triangle, with base 0-60 in. Between values of x = 0 and x = 30, the probability density function has the equation

(a) Sketch the complete PDF. Demonstrate that

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(b) Find the probability that next summer’s rainfall will not exceed 20 in.

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(c) Find the probability that summer rainfall will equal or exceed 30 in. for the next three consecutive summers.

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(d) For the above PDF, what is the mean value of summer rainfall?