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Audrey and Diana go fishing at the Lyndon Fishing Pond. Upon arrival the owner informs...

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Statistics

Audrey and Diana go fishing at the Lyndon FishingPond. Upon arrival the owner informs them that the pond is stockedwith an infinite number of independent fish, and that a typicalfisher catches fish at a Poisson rate of 2 fish per hour. There are10 other people fishing there that day. Diana has the same skilllevel as a typical fisher but Audrey catches on average twice asmany fish as a typical fisher.

(a) (2) Find the mean and variance of the total number of fishcaught over 5 hours.

For the rest of the question, assume that 90 fish were caughtthat day.
(b) (3) Show that we have the following probabilities. Use thoserounded probabilities in parts b), c) and d):
i. The probability a fish was caught by Audrey is 0.154
ii. The probability a fish was caught by Diana is 0.077
iii. The probability a fish was caught by someone else is 0.769

(c) (2) Find the probability that Audrey catches 15 fish andDiana catches 15 fish

(d) (2) Find the probability that Audrey and Diana catch 30 fishtogether

(e) (2) Given that Audrey catches 15 fish, find the probabilitythat Diana catches 15 fish

(f) (2) Explain logically the difference between theprobabilities in (c), (d), and (e)

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