Recall the distribution of hazardous flood rate used in Example 4.5.

a. Obtain the mean and standard deviation of this distribution.
b. What is the probability that the flood rate is within 1 standard deviation of the mean value?

Data From Example 4.5

Transcribed Image Text:

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 fix) 2 0; to show that f(x)dx= 1, we use calculus: 10 [ rusa - [ + ][ me Odx+ 10 f(x) = .04e-04(x-10) x>10 004- -0-(-ee04(10)). ==1 0.02- 0.00 04e04-10)dx=.04e PUX'= 50) met jo 10 -04%dx=04e4. 130 04x100 10