The period (measured in days) over which a patient with COVID-19 who is accepted to a...

 

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The period (measured in days) over which a patient with COVID-19 who is accepted to a hospital will require hospital care is a random vari- able X from an exponential distribution with parameter. Hospital discharges take place only after full days of hospital stay, at the first possible discharge moment when the patient does not require hospital care anymore. By Y we denote the number of days a patient spends in hospital. (a) Find the distribution of random variable Y. Is Y discrete? Is Y continuous? Justify your answer. (b) Find the average amount of time a patient who does not need hospital care stays in the hospital before being discharged. (c) Are random variables X and Y independent? Justify your answer. The period (measured in days) over which a patient with COVID-19 who is accepted to a hospital will require hospital care is a random vari- able X from an exponential distribution with parameter. Hospital discharges take place only after full days of hospital stay, at the first possible discharge moment when the patient does not require hospital care anymore. By Y we denote the number of days a patient spends in hospital. (a) Find the distribution of random variable Y. Is Y discrete? Is Y continuous? Justify your answer. (b) Find the average amount of time a patient who does not need hospital care stays in the hospital before being discharged. (c) Are random variables X and Y independent? Justify your answer.

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