When customers subscribe to a music streaming service, they have 2 options (a) a free service...

 

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When customers subscribe to a music streaming service, they have 2 options (a) a free service (b) a premium service costing $12/month. Based on customer data from the most recent year, the company finds that 70% of new customers choose the free service. At the end of their first month, subscribers have 3 options (i) continue their existing service, (ii) switch to the other service (iii) discontinue the service. The past years customer data also shows that the proportions of customers with the free service in their first month who choose these 3 options are (i) 60% (ii) 30% (iii) 10%. Also, the proportions of customers with the premium service in their first month who choose these 3 options are (i) 80% (ii) 10% (iii) 10%. (a) [1]What method of assessment was used to estimate the proportion (or probability) in the question? (b) [4]What is the probability of a customer dropping the service in their second month? (c) [4]Is dropping the service in the second month independent of having the free service in the first month? (d) [4]What is the probability that a customer had originally subscribed to the free service in their first month given that he/she has the premium service in their second month? (e) [4]What is the probability that a customer has premium service in the first month or premium service in the second month? (f) [4]Assuming that free or discontinued service brings $0 revenue, what is the expecta- tion and variance of revenue from one customer in their first month? (g) [4]What is the Coefficient of Variation of the revenue from one customer in their first month? When customers subscribe to a music streaming service, they have 2 options (a) a free service (b) a premium service costing $12/month. Based on customer data from the most recent year, the company finds that 70% of new customers choose the free service. At the end of their first month, subscribers have 3 options (i) continue their existing service, (ii) switch to the other service (iii) discontinue the service. The past years customer data also shows that the proportions of customers with the free service in their first month who choose these 3 options are (i) 60% (ii) 30% (iii) 10%. Also, the proportions of customers with the premium service in their first month who choose these 3 options are (i) 80% (ii) 10% (iii) 10%. (a) [1]What method of assessment was used to estimate the proportion (or probability) in the question? (b) [4]What is the probability of a customer dropping the service in their second month? (c) [4]Is dropping the service in the second month independent of having the free service in the first month? (d) [4]What is the probability that a customer had originally subscribed to the free service in their first month given that he/she has the premium service in their second month? (e) [4]What is the probability that a customer has premium service in the first month or premium service in the second month? (f) [4]Assuming that free or discontinued service brings $0 revenue, what is the expecta- tion and variance of revenue from one customer in their first month? (g) [4]What is the Coefficient of Variation of the revenue from one customer in their first month?