Bird songs can be characterized by the number of clusters of "syllables" that are strung together in rapid succession. If the last cluster is defined as a "success," it may be reasonable to treat the number of clusters in a song as a geometric random variable. Does the model p_X(k) = (1 − p)^k−1 p, k = 1, 2, . . ., adequately describe the following distribution of 250 song lengths (100)? Begin by finding the method of moments estimate for p. Then calculate the set of "expected" frequencies.

No. of Clusters/Song            Frequency

1……………………………  132

2……………………………   52

3……………………………   34

4……………………………   9

5……………………………   7

6……………………………   5

7……………………………   5

8……………………………   6

……………………………..  250