Question

25.9 The vertical distribution of some marine invertebrates follows a probability di tion with depth p(x) = 2Bxe-Bx, where p > 0. This means that the probabil any particular individual invertebrate is found between depths x and x + x * + Ax mis approximately p(x)Ax. (a) Show that the depth at which the probability density function is maximized (ee tha! depth at which there is the highest probability of finding an invertebratel is x = (28)-2. (b) Multiplying the density function by a constant a gives a function that provides the organism density S(x) =a p(x) at each depth (the units for a will be individuals per bic meter). Find a and B so that the maximum density of 115 organisms per cubig meter occurs at a depth of 35 m. (c) Using the values of a and B found above, and the total number of invertebrates between x=0m and x = 50 m. Hint: Take the integral of S(x) to find this.

Answer 1

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