You are an entrepreneur developing health tracking devices e

You are an entrepreneur developing health tracking devices (e.g., a “fitbit”) for dogs. You want to sell your devices through veterinarians. Suppose that each customer visiting the veterinarian independently purchases a dog health tracking device with probability p = 0.02, and you have already produced 100 prototypes of the dog health tracking device that are ready to be sold.

1,Suppose the veterinarian sees 10 scheduled customers per day for each day of the business week (Monday through Friday). What is the probability that two health tracking devices were sold in the first business week?

2,Given that the second device was sold to the 100th customer, what is the proba- bility that the first device was sold to the 99th customer? why?

Solution

1) The distribution of no of devices sold is Poisson

For 1 week with 10 customers lemda = 10x0.02x7 =1.4

P(x=2) = 0.24167

2) P(x=0 for 98 customers)*P(x=2 in last 2 customers)

= P(x=0 when lemda = 1.96) *P(x=2 when lemda =0.04)

=0.14086(0.0007686)

=0.000108