Ambulance arrives at the emergency department of a large hospital according to a Poisson process at a rate of one arrival every 6 minutes. Each ambulance contains one or more patients; Y, the number of patients in an ambulance, has the probability distribution below. ( the number of patients in an ambulance is independent of the number in any other ambulance)
y 0 1 2 3
P(Y = y) 0.75 0.15 0.05 0.05
a)Find the index of dispersion for this process.
b) Find the variance of the number of patients per ambulance

Question

Ambulance arrives at the emergency department of a large hospital according to a Poisson process at a rate of one arrival every 6 minutes. Each ambulance contains one or more patients; Y, the number of patients in an ambulance, has the probability distribution below. ( the number of patients in an ambulance is independent of the number in any other ambulance)
y          0           1           2             3
 P(Y = y)    0.75     0.15       0.05        0.05 
a)Find the index of dispersion for this process.
b)  Find the variance of the number of patients per ambulance

ybarrap · Answer

If each ambulance has 1 or more patients (and never any fewer), how can P(Y=0) = 0.75?