Topic: Further Properties of Poisson Process 1. The employee of the subscription

Question

Topic: Further Properties of Poisson Process

1. The employee of the subscription magazine publisher records an average of 6 new subscriptions / day, and the number of new subscriptions that register themselves daily follows Poisson. Each new subscription will be a 1-year or 2-year subscription with 2/3 and 1/3 probabilities. If the employee will get an a dollar bonus for each 1 year subscription and b dollar for each 2 year subscription, then specify the expectation of the bonus that will be received during the t day interval?

Explanation / Answer

Here Pr(1 year subscription) = 2/3 ; Benifit = $ 2

Pr(2 year subscription) = 1/3 ; Benefit = $1

Expected nuber of subscription in t days = 6t

Expected NUmber of 1 year subscription among these = 6t * 2/3 = 4t

Expected Number of 2 year subscription among these = 6t * 1/3 = 2t

Expected Total benifit = 4t * 1 + 2t * 2 = 8t

so expected bonus received in t day interval = $ 8t

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