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please help this probability and statistics question with clear steps and also expatiation, thankkk so much 6. Let X. be the number of particles emitted

please help this probability and statistics question with clear steps and also expatiation, thankkk so much

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6. Let X. be the number of particles emitted in t hours from a radioactive source and suppose that X: has a Poisson distribution with parameter at. Let T equal the number of hours until the first emission. Show that T has an exponential distribution with parameter 2. (10 marks)

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