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Mark53
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Homework Statement
From various studies, it is known that once an individual is infected with a virus, they become infectious at rate λ. The individual will recover at rate λ, independent of the time it took for them to become infectious. Let X be the total amount of time an individual has this virus.
(a) What is the distribution of X?
(b) What is the probability an infected individual has this virus for less than 1 day?
(c) If λ = 1, what is the probability that after getting the virus, they become infectious in less than one day and then they recover in less than one day?
The Attempt at a Solution
a)
X~Poi(λ)
b)
P(x<1)=P(x=0)
=e^(-λ)λ^0/0!
=e^(-λ)
c)
P(x<1)nP(x<1)
=P(x=0)*P(x=0)
=e^(-λ)*e^(-λ)
=e^(-2)
not sure if this part is correct