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Unformatted text preview: Stat 230 Assignment 3 - Solutions 1. In a trench in the Pacific Ocean, a particular species of mollusk is distributed according to a Poisson process with an unknown density of λ per cubic meter of water. A sensor is constructed that can detect a chemical emitted by any members of the species that are within 4 meters, and n readings from the sensor are collected over the course of a year to try to measure λ . You may assume that the readings are sufficiently separated that they are independent, so that the number of readings that detect a mollusk has the distribution X ∼ Bi( n,p ) for some unknown value of p . (a) After analyzing the data, it is determined that there was at least one mollusk in range for 700 out of 1000 readings, so p is estimated to be approximately . 70 . i. Express λ as a function of p . (Note: the water within 4 meters of the sen- sors forms a sphere with radius 4 meters. Your expression should involve the volume of this sphere.) ii. Estimate the average number of mollusks within range of the sensor at anyii....
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- Spring '10
- Normal Distribution, Probability theory, probability density function, Cumulative distribution function