Poisson thinning: exactly two large orders

MediumRandom Variables~4m

Orders hit your book as a Poisson process averaging $\lambda = 10$ per hour. Independently, each order is "large" with probability $0.3$ and "small" otherwise. What is the probability of exactly 2 large orders in an hour? Give a decimal to four places.

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Thinning a Poisson stream gives a Poisson stream with rate $\lambda p$ .
Then evaluate the pmf at $k=2$ with rate $10\cdot 0.3=3$ .

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0.224 (± 0.001)

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Poisson thinning: exactly two large orders

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