The vertical distribution of some marine invertebrates follows a probabilitydistribution with depth p(x) = 2Bxe-Bx, where B > 0. This means that theprobability that any particular individual invertebrate is found between depthsx and x + Ax meters is approximately p (x) Ax.(a) Show that the depth at which the probability density function is maxi-mized (e.g., the depth at which there is the highest probability of findingan invertebrate) is x = (28)¯12.(b) Multiplying the density function by a constant a gives a function thatprovides the organism density S(x) = ap (x) at each depth (the units fora will be individuals per cubic meter). Find a and ß so that the maximumdensity of 115 organisms per cubic meter occurs at a depth of 35 meters.(c) Using the values of a and ß found above, find the total number of inver-tebrates between x = 0 and x = 50 meters. Hint: Take the integral of S (x)to find this.

Answered: The vertical distribution of some…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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