NOTE: The QQ plot for the uniform distribution that we looked at in class is under 'Resources' on the homepage. Note that you will need to change the inverse CDF function [F_inverse(p)] so that it corresponds to an exponential RV.

NOTE: The link "Exponential Quantiles & QQ-plot" in the brief intro to JMP has details (using JMP) for the exponential example that we looked at in class.

The time (in minutes) between calls made over a public safety radio were measured on four different days during a one hour period. The observed data (x_obs) in Excel is located at this URL. A researcher wants to know if a Poisson Process is a good model for the data, and if so what the parameter should be for the exponential distribution that is used to model the inter-arrival times.

For the questions below, copy and paste the appropriate output fom Excel into Word.

(a) Find the expected quantiles for the observed data assuming that the parameter for the exponential distribution is theta = 10. List both the observed and expected quantiles.

(b) Calculate the sample mean and sample variance of the observed data. Do these values indicate that an exponential model is a good fit for the data?
Why or why not?
What is your estimate of the "best" exponential RV that could be used to model these data (round your answer to the nearest tenth)?

(c) Create a Q-Q plot of the ordered observations (the observed quantiles, Q_obs) and the expected quantiles (Q_exp). What is your conclusion?