Suppose that the number of spam emails that arrive to your Google account follows a Poisson process with a rate of AG = 2 per hour, the number of spam emails that arrive to your AOL account follows a Poisson process with a rate of d = 1 per hour, and the two Poisson processes are independent. Let V. be the waiting time to have the k th spam email in your Google account, and let W. be the waiting time to have the k th spam email in your AOL account. What is the probability that the waiting time to have the 2nd spam email in your Google account is longer than the waiting time v Choose... to have the 1st spam email in your AOL account, i.e., P(V½ >W1) ? 4 5/9 What is the expected number of spam emails that arrive to your Google account from 9:00am to 1:00pm? 6 2/3 What is the expected waiting time to have the 5th spam email in your Google account from 9:00am, given that the first spam email has arrived at 10:00am? 8 1/3

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