Solution Found!
An article in Mathematical Biosciences [“Influence of
Chapter 4, Problem 152E(choose chapter or problem)
An article in Mathematical Biosciences [“Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients” (1998, Vol.152(2), pp. 143–163)] considered the time delay between the initial infection by immunodeficiency virus type 1 (HIV-1) and the formation of productively infected cells. In the simulation model, the time delay is approximated by a gamma distribution with parameters r = 4 and \(1 / \lambda=0.25\) days. Determine the following:
(a) Mean and variance of time delay
(b) Probability that a time delay is more than half a day
(c) Probability that a time delay is between one-half and one day
Equation transcription:
Text transcription:
1 / lambda=0.25
Questions & Answers
QUESTION:
An article in Mathematical Biosciences [“Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients” (1998, Vol.152(2), pp. 143–163)] considered the time delay between the initial infection by immunodeficiency virus type 1 (HIV-1) and the formation of productively infected cells. In the simulation model, the time delay is approximated by a gamma distribution with parameters r = 4 and \(1 / \lambda=0.25\) days. Determine the following:
(a) Mean and variance of time delay
(b) Probability that a time delay is more than half a day
(c) Probability that a time delay is between one-half and one day
Equation transcription:
Text transcription:
1 / lambda=0.25
ANSWER:Solution:
Step 1 of 4:
The time delay is approximated by a gamma distribution with parameters r=4 and = 0.25.
- We have to find the mean and variance of the time delay.
- We have to find the probability that a time delay is more than half a day.
- We have to find the probability that a time delay is between one- half and one day.