The data presented in the table for Problem are known as grouped data, of the type that ar...

The data presented in the table for Problem are known as grouped data, of the type that are developed in order to plot a frequency histogram. The mean of such data can be determined as a weighted average of the class marks, as follows:

where f and ti are the frequency and class mark, respectively, for k class intervals.

(a) Demonstrate that the mean of the interevent times of Problem is as stated.

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(b) How many interevent time values were used in the analysis?

Problem

Interevent times for winter storms arriving at Corvallis, Oregon, for the months November through April for the winters of 1996-97, 1997-98, and 1998-99 were determined, and a frequency histogram prepared as shown in the table below. The average interevent time was 2.59 days.

(a) Fit an exponential distribution to these data by finding the parameter λ.

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(b) Plot the relative-frequency histogram and the fitted exponential PDF on the same chart. Care may need to be taken to be sure that the histogram and PDF are properly aligned. Each day (0-1, 1-2, and so on) is a class interval.

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(c) From the relative-frequency histogram, compute the cumulative-frequency histogram and plot on arithmetic graph paper.

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(d) On two-cycle semilog paper (or using spreadsheet options for log-scales), plot the empirical CDF from part (c) and the fitted CDF. On this “probability paper,” values should be plotted at the class mark, centering on half-days. The empirical values from part (c) should be plotted as individual points, and one fitted CDF (exceedance probability) should be plotted as a straight line.

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(e) What is the probability that the time between winter storms is ≤ days? Compute using both the empirical CDF and the fitted CDF.