Assume that Alice will arrive home this evening at a random time, uniformly distributed between 5pm and 6pm. Bob promises to call Alice “after 5pm”, which means Bob will wait an exponential amount of time after 5pm with expected value 30 minutes and then call Alice. Assume the time Alice arrives home is independent of the time when Bob will call.
(a) Compute the probability that Alice will not miss Bob’s call.
(b) Compute the probability that Bob will call before 6, given that Alice does not miss Bob’s call.
Assume that Alice will arrive home this evening at a random time, uniformly distributed between 5pm...
The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0, 12]. You observe the wait time for the next 100 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 100 wait times you observed is between 565 and 669? Part b) What is the approximate probability (to 2 decimal places) that the average of the...
Exercise 8. Alice and Bob are supposed to meet at 2pm. The number of hours Alice is late is distributed uniformly over (0, 2). The number of hours Bob is late is distributed according to an exponential random variable with parameter 1. Their respective delays are supposed to be independent. Let X be the time at which Alice and Bob actually meet (in number of hours after 2pm). (a) (4 points) Find the cumulative distribution function of X. (b) (2...
The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 95 trains to arrive. Assume wait times are independent Use the Normal approximation to the Binomial distribution (with continuity correction) to find the probability (to 2 decimal places) that 56 or more of the 95 wait times recorded exceed 5minutes
The time a bus will arrive is uniformly distributed from 8:00 AM until 8:20 AM. You arrive at the bus stop at exactly 8:00 AM. What is the probability you will wait 12 minutes or more?
A shop has an average of five customers per hour 5. A shop has an average of five customers per hour (a) Assume that the time T between any two customers' arrivals is an exponential random variable. (b) Assume that the number of customers who arrive during a given time period is Poisson. What (c) Let Y, be exponential random variables modeling the time between the ith and i+1st c What is the probability that no customer arrives in the...
Can you solve 12 Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note that it is wrong to reason like this: Alice expects to arrive at 12:30, Bob expects to arrive at 1:00: thus, we expeet that Bob will wait 30 mimutes for Alice.) (b). We want to compute the probability that Bob has to wait for Alice, which is P(Y < X), which we do by integrating the joint density, f(r,y), over the region where <...
For a passenger who arrives at a certain bus stop at a random moment in time, the time spent waiting for the bus is uniformly distributed from 0 to 9 minutes. What is the probability someone who arrives at this bus stop at a random moment will wait at least 7 minutes for the bus? (Round to the nearest tenth of a percent.)
Exercise 2.3 The time between phone calls to a call center is exponentially distributed with mean 60 seconds. (a) What is the probability that exactly 4 calls arrive in the next 2 minutes? (6) What is the probability that at least 2 calls arrive in the next 2 minutes? (c) What is the probability that no buses arrive in the next 2 minutes? (d) Given that a call has just arrived, what is the probability that the next call arrives...
The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 5 minutes. A) What is the probability that more than three customers arrive in 10 minutes? B) What is the probability that the time until the 6th customer arrives is less than 5 minutes?
7. Assume requests arrive at a web site one by one at random intervals, and the time between the arrivals of consecutive jobs are observed to have an exponential distribution. The average arrival rate is measured to be 4 requests per second. Assume a request has arrived at time. What is the probability that the next request arrives after I by at least 200 msec, but before 300 msec elapses? Uddal