Negative Binomial and Chi-square

[sam_0017]

can anyone help me with this question :

 

[Stephen Tashi]

I haven't looked at the problem closely. Is there some difficulty in solving the simultaneous equations for p and k ?

$$\bar{x} = \frac{ k(1-p)}{p}$$
$$s^2 = \frac{k(1-p)}{p^2} = \frac{\bar{x}}{p}$$