Respuesta :
Answer:
a. Probability the reservoir will be empty after five days
e-1.5 + 0.6 e-1.5 e-1.5
b. Probability the reservoir will be empty sometime within the next ten days
Probability of rain falls in next ten days = 10 x 0.4
=4
Step-by-step explanation:
The water level of the reservoir is depleted at a constant rate of 1000 units daily.
Rainfalls occur to the Poisson process with a rate of 0.3 per day.
a) Probability the reservoir will empty after five days is when there is no rain in the next five days.
Rainfall rate = 0.3 per day
Expected rain fall = 5 x 0.3 =1.5
Mean = µ =1.5, rain fall =x = 0
By using Poisson distribution formula, we get
P (empty) =p( empty at 5 day) + p (1.5 x 5000) x p(empty in 5 day)
= e-1.5 + 0.6 e-1.5 e-1.5
b)
The next ten days reservoir will be empty if there will be no rain.
There will be one rain of 5000 units in the next ten days.
Probability of rain falls in next ten days = 10 x 0.4
=4
Hence, four is the probability of rain falls in the next ten days
