A release-checked medium problem for training Continuous Random Variables.
Question
Two quant firms have client inflow that is well-modeled by independent Poisson processes. The respective intensity parameters are $6$ and $10$. Clients give outstanding reviews about the service with respective probabilities $\dfrac{1}{6}$ and $\dfrac{1}{5}$ for the two firms, independent of one another. The clients that give outstanding reviews are sent a thank you card. Find the expected time between clients that receive thank you cards.
Practice focus
This Probability problem is tagged Continuous Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.