Buyer count in a thinned arrival stream

MediumProbability Stochastic Processes~4m

Customers arrive as a Poisson process at rate $\lambda = 10$ /hour; each is independently a buyer with probability $0.2$ . What is the probability that exactly $3$ buyers arrive in a $90$ -minute window? (to 3 decimals)

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Thinning gives a Poisson process at rate $p\lambda$ ; then scale to the window length.
Evaluate $\text{Poisson}(\mu)$ at $k=3$ with $\mu=p\lambda t$ .

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0.224 (± 0.005)

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Buyer count in a thinned arrival stream

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