5. Studies of marine extinction rates in the fossil record show that over the past 562 million years, there have been 2,230 extinction events over 76 distinct geological epochs. Suppose that that these events can be modeled as a Poisson process. (a) Find X for the entire 562 million year period. What are the ca = .05 condence limits on your estimate? (b) (Recall last quarter.) A X2 test for homogeneity, assuming that the rate is uniform across all epochs, gives X2 = 1,565. State the number of degrees of freedom, the expected value of )8, and the pvalue resulting from the observed X2 for the homogeneity hypotheses using the tables in the back of Rice. (0) Now do a little inference on Specic individual epochs while regarding extinctions in each epoch as Poission, but possibly having different rates. Between 86 and 82 million years ago, there were 18 extinctions. Between 65 and 70 million years ago there were 82 extinctions. Find the extinction rate for both of these epochs and determine their condence intervals. How does this relate to your ndings in the previous 2 parts of this