Question: 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

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 and the probability density function has the equation
f(x) = x/900 ,0 ≤ x ≤ 30
(a) Sketch the complete PDF. Demonstrate that ∫ f(x) dx = 1.0
(b) Find the probability that next summer's rainfall will not exceed 20 in.
(c) Find the probability that summer rainfall will equal or exceed 30 in. for the next three consecutive summers.
(d) For the above PDF, what is the mean value of summer rainfall?

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