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1. In the table of the text above, we recorded observations for what we believed to be a loaded…

1. In the table of the text above, we recorded observations for what we believed to be a loaded…

1. In the table of the text above, we recorded observations for what we believed to be a loaded die. Suppose, instead, we had thought the die fair. Would the data have suggested that, in fact, it was not fair?2. With X2 we have a way to test fit to the Poisson distribution for Bortkiewicz' data on horsekick fatalities. Bortkiewicz, you will recall, was the first person to realize that Poisson's abstractly derived distribution would model real-world situations. In the leftmost table below, we give Bortkiewicz' data. Recall that we estimated A, the average number of horsekick fatalities per corps-year, from Bortkiewicz' data. That gave λ ≈ 0.61. In the table on the right, we give that Poisson distribution through X = 4.(a) Calculate the expected number of corps-years for each of the five values of B, assuming the Poisson distribution with λ = 0.61. (b) Evaluate Bortkiewicz' observed value of X2. (c) Does the Poisson model seem to fit Bortkiewicz' data? (d) Give a verbal description of the p-value calculated in part (b).