Question

According to a recent survey, the number of Corona affected patients is increasing at an alarming rate (8 persons per day) in a particular residential sector of Islamabad city. Keeping in view that the inter arrival time within events of desired interest is independently and exponentially distributed, determine the following:

1. What is the average time between two successive reported cases in that area?
2. Given a case (Corona affected patient) has already been reported, what is the probability that the next patient case is reported within 06 hours?
3. What is the probability that there is at least a 12 hours gap between two reported patients?
4. What is the probability that the particular sector in Islamabad reports 50 Corona cases in a single day?

NOTE= kindly attempt all parts (requested)

Answer 1

Rate of affected patients, = 8 persons per day

(a) Average time between two successive reported cases in that area = 1/8 days = 3 hours

(b) The event of next patient case being reported is independent of any previous case being reported

The required probability = P(T < 6)

Here T is exponentially distributed with mean = 3 hours

Thus, P(T < 6) = = 0.8647

(c) The required probability = P(T ≥ 12)

= = = 0.0183

(d) The probability that the particular sector in Islamabad reports 50 Corona cases in a single day = P(X = 50)

= poissonpdf(8, 50)

= 1.574E-23