Hello tutors, can I please get assistance with the following probability problem? Thank you.

Do extinctions occur randomly through the long fossil record of Earth's history, or are there periods in which extinction rates are unusually high ("mass extinctions") compared with background rates? Whitlock and Schluter (2009) give the following data on the number of extinctions of marine invertebrate families in 76 blocks of time of similar duration:

0 extinctions happened in none of the blocks

1 extinction happened in 13 blocks

2 extinctions happened in 15 blocks

3 extinctions happened in 16 blocks

4 extinctions happened in 7 blocks

5 extinctions happened in 10 blocks

6 extinctions happened in 4 blocks

7 extinctions happened in 2 blocks

8 extinctions happened in 1 block

9 extinctions happened in 2 blocks

10 extinctions happened in 6 blocks

How would you estimate the expected number of extinctions per block given the data above and compare the proportion of blocks predicted by the model for each of the above extinction numbers with the observed ones? Is there much difference between the two?

After providing those in a table, how would you make a chi-square test by adding the counts to the table, both the counts observed and the predicted ones.

Hint:

The theoretical Poisson model is first assumed for the number of extinctions per block. Call this random variable X. We do not know the parameter, but a statistician would estimate it given the data. A good estimate would be the average number of extinctions per block.

()= (1)(13)+(2)(15)+3(16)++9(2)+10(6)76=3.855263

If a data set was generated by a Poisson model with parameter =3.855263=3.855263,the probabilities of observing the values of X observed above would be given by .... (you continue from here on).