Consider again the rv X = hazardous flood rate given in Example 4.5. What is the probability that the flood rate is

a. At most 40 m³/s?
b. More than 40 m³/s? At least 40 m³/s?
c. Between 40 and 60 m³/s?

Example 4.5.

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Example 4.5 Climate change has made effective modeling and management of floodwaters ever more important in coastal areas. One variable of particular importance is the flow rate of water above some minimum threshold (typically where the rate becomes hazardous and requires intervention). The following pdf of X = hazardous flood rate (m³/s) is suggested under certain conditions by the article "A Framework for Probabilistic Assessment of Clear-Water Scour Around Bridge Piers" (Structural Safety 2017: 11-22): The graph of f(x) is given in Figure 4.4; there is no density associated with flow rates below 10 m³/s, because such flow rates are deemed nonhazardous under these particular conditions. The flow rate density decreases rapidly (exponentially fast) as x increases from 10. Clearly f(x) > 0; to show that f(x) dx = 1, we use calculus: Ĵro f(x) dx = [ 0.04 The graph of f(x) is given in Figure 4.4; there is no density associated with flow rates below 10 m³/s, because such flow rates are deemed nonhazardous under these particular conditions. The flow rate density decreases rapidly (exponentially fast) as x increases from 10. Clearly f(x) > 0; to show that f(x)dx= 1, we use calculus: 0.02 -.04x .04(x-10) 0dx+ -100+ [4e-a-me² ] 0 dx = .04e-4 -∞ 10 = 0- )-(-eª. -.04(10) · e 0.00 f(x) = .04e-04(x-10) f(x) = .04e-04(x-10) 10 10 .04e 30 = 1 x>10 P(X ≤ 50) 50 x ≥10 70 T 90 110 dx - .04e-4. T 130 -.04.x|∞ .04 10