Combined Poisson Processes - Quant Trader Interview Question
Difficulty: Easy
Category: Probability & Statistics
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Topics: probability, poisson-process, additivity, statistics
Problem Description
Two independent trading algorithms generate buy orders. Algorithm A generates orders according to a Poisson process with an average rate of 3 orders per minute. Algorithm B generates orders according to a Poisson process with an average rate of 5 orders per minute. What is the distribution of the total number of buy orders generated by both algorithms in one minute?
Assume $X$ is number of orders from Algorithm A and $Y$ is number of orders from Algorithm B. $X \sim Pois(\lambda_1)$ and $Y \sim
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