A lake contains 10 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least 5 distinct types of fish. (hint: For geometric distribution with parameter p, its expectation and variance are respectively 1 /p and 1−p/p2 . (a) Give an interval (a, b) such that P(a ≤ Y ≤ b) ≥ 0.90. (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least 5 distinct types of fish.
A lake contains 10 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least 5 distinct types of fish. (hint: For geometric distribution with parameter p, its expectation and variance are respectively 1 /p and 1−p/p2 . (a) Give an interval (a, b) such that P(a ≤ Y ≤ b) ≥ 0.90. (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least 5 distinct types of fish.
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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A lake contains 10 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least 5 distinct types of fish. (hint: For geometric distribution with parameter p, its expectation and variance are respectively 1 /p and 1−p/p2 .
(a) Give an interval (a, b) such that P(a ≤ Y ≤ b) ≥ 0.90.
(b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least 5 distinct types of fish.
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