A telemarketing salesperson makes a series of telephone calls, some of which (successful calls) result in...

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A telemarketing salesperson makes a series of telephone calls, some of which (successful calls) result in a sale, while others (unsuccessful calls) do not. The salesperson must fulfill a daily quota of 5 successful calls. On a given day, the number Y of unsuccessful calls made before this quota is fulfilled follows this particular negative binomial distribution: YO NegBinomial (0, m = 5) in the notation of BSM, Appendix A.1. Here, 0 <0<1, but is otherwise unknown. (a) [1 pt] Considering this scenario, describe briefly in words what 0 represents, in practical terms. (b) [1 pt] If it were true that 0= 0.2, what would be the expected total number of calls the salesperson would need to make (including both the successful and unsuccessful calls) to fulfill the daily quota? (c) [2 pts] Yesterday, the salesperson made y = 20 unsuccessful calls before fulfilling the quota. Give an expression for the likelihood function of 0 (up to proportionality) based on y. (d) [2 pts] Assume a uniform ("flat") prior for 0. Using the likelihood of the previous part, derive an expression for the posterior density (up to proportionality). (e) [2 pts] Identify the posterior distribution corresponding to the density you derived in the previous part. (Name it and specify the values of its constants.) A telemarketing salesperson makes a series of telephone calls, some of which (successful calls) result in a sale, while others (unsuccessful calls) do not. The salesperson must fulfill a daily quota of 5 successful calls. On a given day, the number Y of unsuccessful calls made before this quota is fulfilled follows this particular negative binomial distribution: YO NegBinomial (0, m = 5) in the notation of BSM, Appendix A.1. Here, 0 <0<1, but is otherwise unknown. (a) [1 pt] Considering this scenario, describe briefly in words what 0 represents, in practical terms. (b) [1 pt] If it were true that 0= 0.2, what would be the expected total number of calls the salesperson would need to make (including both the successful and unsuccessful calls) to fulfill the daily quota? (c) [2 pts] Yesterday, the salesperson made y = 20 unsuccessful calls before fulfilling the quota. Give an expression for the likelihood function of 0 (up to proportionality) based on y. (d) [2 pts] Assume a uniform ("flat") prior for 0. Using the likelihood of the previous part, derive an expression for the posterior density (up to proportionality). (e) [2 pts] Identify the posterior distribution corresponding to the density you derived in the previous part. (Name it and specify the values of its constants.)