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Sagot :
The mean number of servers that fail is E[X] = np = 3.
Given,
In the question:
A data center contains 1000 computer servers.
and, each server of failing has probability is 0.003
To find the probability that exactly two servers fail.
Now, According to the question:
Suppose that serves fails independently
We use the formula of Binomial Distribution B(n, p),
where, n=1000, p=0.003:
P(X = k) =( [tex]\left \({ {{n} \atop {k}} \right.)[/tex] [tex]p^{k}[/tex][tex](1 - p)^n^-^k[/tex]
Substitute the values :
P(X = 2) = [tex]\frac{1000.999}{2}[/tex][tex]0.003^2.0.997^9^9^8[/tex]
We can calculate it:
But you should know that in this case the distribution is closer to Poisson
distribution
λ = np
Probability P(X = k) = λ^k/k! ×e^-λ
P(X =2) = [tex]\frac{3^2}{2!}e^-^3[/tex]
As for the second question: it is equivalent to 3 or more failed servers, so the probability is:
1 - (P(X = 0) + P(X = 1)+ P (X = 2)) ≈ 1 - (1+ 3 + [tex]\frac{9}{2}[/tex])[tex]e^-^3[/tex]
Hence, The mean is E[X] = np = 3.
Learn more about Probability at:
https://brainly.com/question/26650929
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