10. Individuals 1 through n, n > 1, are to be recruited into a firm in the following manner. Individual 1 starts the firm and recruits individual 2. Individuals 1 and 2 will then compete to recruit individual 3. Once individual 3 is recruited, individuals 1, 2, and 3 will compete to recruit individual 4, and so on. Suppose that when individuals 1, 2, i compete to recruit individual i + 1, each of them is equally likely to be the successful recruiter.

(a) Find the expected number of the individuals 1,..., that did not recruit anyone else.

(b) Derive an expression for the variance of the number of individuals who did not recruit anyone else and evaluate it for n 5.

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