2.10∗ Verify the results of Section 2.3, that under the beta-geometric model, the expected remaining waiting time for couples who have had j failed cycles is given by:

E[(X − j)|X>j] =  1 − θ

μ − θ



+ jθ

(μ − θ) .

Hint: First of all show that under the beta-geometric model, conditional upon the event X>j, the distribution of the parameter p is Be μ

θ

, 1 − μ

θ + j



.