Data was recorded on 150 workplace accidents The number of d

Data was recorded on 150 workplace accidents. The number of days since the previous accident is summarized in the following table

We want to check to see if a geometric model is appropriate for this data. P{X = x} = p(1 ? p) x

(a) Show that the MLE for this model is ˆp = 1/(¯x + 1).

(b) Calculate the MLE for p from the given set of data.

(c) Calculate the expected value for each number in this table if this data is from a geometric distribution.

(d) Is our rule of thumb satisified? How can we remedy the situation?

(e) Perform the ? 2 test to see if the geometric model is appropriate.

(f) Find the appropriate critical value for this test using the right number of degrees of freedom and ? = 0.05.

(g) What do we conclude?

Solution