Suppose a nail salon opens at 10am. People start arriving at 9 am and queue in front of the salon. The arrivals follow a

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answerhappygod
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Suppose a nail salon opens at 10am. People start arriving at 9 am and queue in front of the salon. The arrivals follow a

Post by answerhappygod »

Suppose a nail salon opens at 10am. People start arriving
at 9 am and queue in front of the salon. The arrivals follow a
non-homogeneous Poisson process with rate function λ(t) = 25t^2 (t
= 0 refers to 9 am and t = 1 to 10 am). If we know that exactly 30
people are waiting in front of the salon at 10 am, what is the
probability that exactly 20 of them arrived between 9.30am and 10
am?
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