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3. The data below represents the elapsed time, in months, between 37 consecutive eruptions of a certain volcano: 126 73 3 6 37 23 73 23 2 65 94 51 26 21 6 68 16 20 6 18 6 41 40 18 41 11 12 38 77 61 26 3 38 50 91 12 Over the time period covered by this data, eruptions were occurring at the rate of X = 0.027 eruptions per month. Is the data consistent with the model for waiting times between Poisson events with average rate A? To answer this question, first create a frequency histogram of the data with classes [0,20), [20, 40), [120,140). From this, construct a density histogram by replacing the frequency in each class with the density frequency density = class width x total number of observations This produces a histogram in which the total area under the bars is necessarily 1, making it comparable in scale to a pdf. Finally, simultaneously plot the density histogram and the pdf for the waiting times for this model. Does there appear to be good agreement?

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%So, number of eruptions per year follows Poisson process model and hence,
%subsequently, probability of time elapsed and eruption occuring are
%related by exponential distribution(CDF). From this, we derive the PDF by
%classical method of subtracting CDF for the class edges. Thus plot is
%produced.
clear; clc; close all;
X = [126 73 3 6 37 23 73 23 2 65 94 51 26 21 6 68 16 20 6 18 6 41 40 18 41 11 12 38 77 61 26 3 38 50 91 12];
lambda = 0.027;
class_width = 20;
edges = 0:class_width:140;
nTot = length...

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