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A lake contains n fish. A sample of m fish (m

A lake contains n fish. A sample of m fish (m

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Statistics and Probability
Estimating the size of a fish population A lake contains n fish. A sample of m fish (m <n) is caught; the fish are marked, and all are then returned to the lake. Later, a second sample of k fish (k <n) is caught. Making reasonable assumptions about the way in which the sampling would be carried out, find an expression for Pr(X = x ), where X is the number of marked fish in the second sample. This probability is a function of the known quantities k and m, the number x of marked fish in the second sample, and n, which will often be unknown in practice. Viewing Pr(X = x) as a function g (n) of n, examine the ratio g (n)/ g (n – 1) and hence obtain the value of n for which 8 (n) is a maximum.
Transcribed Image Text:Estimating the size of a fish population A lake contains n fish. A sample of m fish (m <n) is caught; the fish are marked, and all are then returned to the lake. Later, a second sample of k fish (k <n) is caught. Making reasonable assumptions about the way in which the sampling would be carried out, find an expression for Pr(X = x ), where X is the number of marked fish in the second sample. This probability is a function of the known quantities k and m, the number x of marked fish in the second sample, and n, which will often be unknown in practice. Viewing Pr(X = x) as a function g (n) of n, examine the ratio g (n)/ g (n – 1) and hence obtain the value of n for which 8 (n) is a maximum.
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