I was a bit confused about this question.
You’re clearing out your garage for a garage sale, and you want to get rid of as much stuff as possible quickly. You found a dresser and decided to sell it to the first person offering 220 or more. Assume offers to buy the dresser are independent exponential random variables with a mean of 150. The price is firm, and you keep taking offers until you receive one that is at least 220.
Given you only accept offers at or above $220, how much money do you expect to get for your dresser?
To solve this, I first calculated the probability that any single offer is too low. I did this by just using the CDF of an exponential with mean 1/150 and P(X < 220) (not sure if this is right, or if I should do a summation). But I'm not sure how to calculate the amount of money I should expect. I'm assuming I need to find some E[X].