What distribution would fit this data?

a-Is it a member of the exponential family?

b-What is the systematic component (linear predictor)? express the mean in terms of the systematic component

c-Briefly describe how you would estimate these parameters based on (b)?

Beta Particles	Frequency
0	55
1	201
2	381
3	523
4	530
5	406
6	271
7	137
8	43
9	25
10	8
11	2
12	0
13	1
14	1
15	0