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Problem 38

Expected animal abuse

Due: February 9
Points: 1

The veterinarian tells you to feed your dog twice a day, once every 12 hours. This will keep the dog healthy and happy. In any case, the vet tells you to always definitely make sure you feed the dog at least once per 24-hour period or else Sparky might starve.

However, you can never remember when is the last time you've fed the dog, and you have a hard time keeping to a fixed schedule. So you devise the following randomized algorithm: Every hour at the top of the hour, you feed Fido with probability 1/12. This way, the expected number of times your dog is feed per day is twice.

(Assume that you never sleep, and neither does your dog, and the meals are always consumed immediately and entirely, etc.)

Do you think this is a good idea? Why or why not? I'm not really interested in your opinion of the dog's feelings or emotional well-being, just with their health.

(Yes, I realize that Rex's name keeps changing.)