Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10messages per hour.
a) What is the probability that hte first message arrives in the first 5 minutes? (randome variable time)
b) What is the probability that 3 messages arrive in 20 minutes? (random variable # of messages)
a)
lambda = 10 per 60 mins
For 5 mins, lambda = 10/12
Here, λ = 0.8333 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x *
e^(-λ)/x!
We need to calculate P(X = 1)
P(X = 1) = 0.8333^1 * e^-0.8333/1!
P(X = 1) = 0.3622
Ans: 0.3622
b)
for 20 mins, lambda = 10/3 = 3.33
Here, λ = 3.3333 and x = 3
As per Poisson's distribution formula P(X = x) = λ^x *
e^(-λ)/x!
We need to calculate P(X = 3)
P(X = 3) = 3.3333^3 * e^-3.3333/3!
P(X = 3) = 0.2202
Ans: 0.2202
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