~if calls to your cell phone are a Poisson process with a constant rate lambda=2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? ~How many phone calls do you expect to get during the movie?
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- Assume that arrivals of cars at a gas station can be modeled by a Poisson process with rate 2 cars per hour. What is the probability that one has to wait at least 3 hours for the arrival of 3 cars?The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are more than two calls in a 20 minutes interval?Suppose the average number of customers going through a drive-thru in a one hour period is 30 and follows a Poisson process. What is the probability that the person working the drive-thru window has to wait more than 32 minutes for 8 customers come through?
- The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are no calls within a one-hour interval?The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are no calls within 20 minutes?The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.
- On Monday mornings, the First National Bank only has one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a four-minute interval on Monday mornings is 1.8, and each teller can serve more than that number efficiently. These random arrivals at this bank on Monday mornings are Poisson distributed. Find the probability that within four minutes interval at least one customer will arrive.an old house in philadelphia is inhibited by a variety of ghosts. appearances occur in the house according to a poisson process having a rate of 1.4 ghosts per hour. A professor from transylvannia university has developed a device which can be used to detect ghost appearances. suppose the device is developed is to be installed in the house and switched on at 8 am what is the probability that the 4th ghost appears more than 30 minutes after the 3rd ghostSuppose the number of photons emitted by an atom during a one-minute time window can be modeled as a Poisson random variable with parameter λ = 2. Now, suppose you watch the atomfor two minutes, and the number of emitted photons in each minute is an independent Poisson process. Calculate the probability that you see exactly one photon during the two minutes. (Hint: this is the probability that you see no photons in the first minute and one photon in the second minute, plus the probability that you see one photon in the first minute and no photons in the second minute.) Similarly calculate the probability that you see exactly two photons during the two minutes.Compare these probabilities to the probabilities that a Poisson random variable with parameter λ= 4 takes the value one, or two. Are they the same?
- Two Poisson processes with rates λ1=6.507and λ2=0.368 resulted from splitting a Poisson process. What is the probability that an arrival from the "parent" process will belong to the second process with rate λ2? Specify your answer to four decimal places.Vahe, who is professor Madoyan’s favorite student, asks questions during office hours with a rate of 2.5 questions per 30 minutes. Suppose that the number of questions asked by Vahe follows Poisson distribution. What is the probability that during 45 minutes OH session, Vahe will ask more than 3 questions (round to 3 decimal places)?From past experience, it was found out that in a certain factory, there is an average of two accidents per' month. Assuming a Poisson distribution, determine the probability that in a certain month selected at random there would be:no accident;exactly two accidents;less than four accidents.