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3. While taking a daily one-hour walk, a person finds coins on the ground according to a Poisson process at a rate of 30 coins per hour, 60% of the coins are pennies, 20% are nickels and 20% are dimes. a. Determine Poisson process rate for each type of coin. b. What is an expression for the value of the coins found during an hour (Use P for number of pennies, N for number of nickels and D for number of dimes and express your answer where monetary values are in cents). What is the expected value of the coins found during an hour? What is the variance of the value of the coins found during an hour? Determine the Poisson process rate for the number of dimes found in a 10 minute period (1/6 hour) Determine the probability of finding exactly two dines in a 10 minute period. Determine the probability of finding at least two dimes in the first 10 minutes and at least three dimes in the first 20 minutes (Hint: You will need to consider two cases, the probability of finding at least 3 dimes in the first 10 minutes and the probability of finding exactly 2 dimes in the first 10 minutes and at least one dime in the next 10 minutes. Remember that for Poisson processes, non-overlapping intervals are independent. c. d. e. f. g.
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