Question: Suppose an infinitely large bucket is being filled with kool-aid continuously with rate 1 Liters/min. Two bartenders serve drinks according to independent Poisson Processes with

Suppose an infinitely large bucket is being filled with kool-aid continuously with rate 1 Liters/min. Two bartenders serve drinks according to independent Poisson Processes with rates 2 drinks/min (Bartender A) and 3 drinks/min (Bartender B). Whenever they serve a drink, they empty the shared bucket into the glass and serve that. Say this process started infinitely in the past.

1. Suppose you come in at a random time, cut to the front of the line, and take the next drink that is served by either bartender. What is the expected volume of the drink you get?

2. Suppose you come in at a random time, again cut to the front, but insist on taking the next drink served by Bartender A. What is the expected volume of the drink you receive?

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