(Answered) Question joe is waiting in continuous time for a book

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Question: Joe is waiting in continuous time for a book called The Winds of Winter to be released. Suppose that the waiting time T until news of the book's release is posted, measured in years relative to some starting point, has an Exponential distribution with λ = 1/5. Joe is not so obsessive as to check multiple times a day; instead, he checks the website once at the end of each day. Therefore, he observes the day on which the news was posted, rather than the exact time T. Let X be this measurement, where X = 0 means that the news was posted within the first day (after the starting point), X = 1 means it was posted on the second day, etc. (assume that there are 365 days in a year). Find the PMF of X. Is this a named distribution that we have studied?

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