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The number of messages sent to a computer website is a Poisson random variable with a mean of 5 messages per hour.
a. What is the probability that 10 messages are received in 1.5 hours?
b. What is the probability that fewer than 2 messages are received in 0.5 hour?
c. Let Y be the random variable defined as the time between messages arriving to the computer bulletin board. What is the distribution of Y? What is the mean of Y?
d. What is the probability that the time between messages is less than 5 minutes?
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