### Statistical Study of Trout Weights for Fish Farming Decisions#### Problem Statement:A fish farmer is investigating the weight distribution of trout in a lake to decide whether to net the lake and sell the fish. A sample of 100 fish was collected and weighed, yielding the following results:#### Data:The weights of the fish are organized in two tables, representing different weight ranges and their corresponding frequencies.| Weight, \( W \) (kg) | Frequency ||----------------------|-----------|| 0 < \( W \) ≤ 0.5 | 2 || 0.5 < \( W \) ≤ 1.0 | 10 || 1.0 < \( W \) ≤ 1.5 | 23 || 1.5 < \( W \) ≤ 2.0 | 26 || Weight, \( W \) (kg) | Frequency ||----------------------|-----------|| 2.0 < \( W \) ≤ 2.5 | 27 || 2.5 < \( W \) ≤ 3.0 | 12 || 3.0 < \( W \) | 0 |#### Analysis:(i) **Histogram Construction and Data Distribution:**To represent the data visually, a histogram should be created using the frequency values and corresponding weight intervals. The vertical axis will represent the number of fish (frequency), and the horizontal axis will represent the weight ranges (kg). The shape of the histogram will help in determining whether the data is symmetrical, positively skewed, or negatively skewed.(ii) **Proposed Probability Density Functions (p.d.f.s):**A friend of the farmer suggests modeling the weight \( W \) as a continuous random variable, proposing four possible p.d.f.s:\[ f_{1}(w) = \frac{2}{9} w (3 - w) \]\[ f_{2}(w) = \frac{10}{81} w^2(3 - w)^2 \]\[ f_{3}(w) = \frac{4}{27} w^2(3 - w) \]\[ f_{4}(w) = \frac{4}{27} w (3 - w)^2 \]These functions are defined for \( 0 < W \leq 3 \).(iii) **

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Description: ### Statistical Study of Trout Weights for Fish Farming Decisions#### Problem Statement:A fish farmer is investigating the weight distribution of trout in a lake to decide whether to net the lake and sell the fish. A sample of 100 fish was collected

The given table: Weight, W Frequency 2 10 23 26 27 12 0 The histogram…

Answered: weighs them. The results (in kg) are as…

Math

Advanced Math

weighs them. The results (in kg) are as follows. Weight, W Frequency Weight, W Frequency 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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