5. Suppose that the time (in hours) that Isabel spends on an untimed final exam exponential distribution with mean 1.25 hours, and the time that Javier spends follows an exponential distribution w...
Suppose that the time (in hours) that Adam spends on an untimed final exam follows an exponential distribution with mean 1.75 hours, and the time that Ben spends on the same exam follows an exponential distribution with mean 2.25 hours. Assume that their times are independent of each other. Using appropriate notation for random variables and events: a) Determine the probability that Ben finishes in less than 2 hours. (Show your work; you may use either the pdf or cdf.)...
IV. Continuous Distribution: Normal Normal 1. The average time to complete a final exam in a given course is normally distributed. With average of 80 min, and standard deviation of 8 minutes. For a certain student taken at random: to. What is the probability of finishing the exam in an hour or less? b. What is the probability of finishing the exam between 60 min and 70 min? Exponential 2. The time to fail in hours of a laser beam...
a hotel, time to process a client's request follows an exponential distribution with a mean of 2.5 minutes a. Find the probability that a given request takes more than 5 minutes to process. b. Find the probability that a given request takes less than 30 seconds to process. c. Find the probability that a given request takes between I and 2.5 minutes to process.
. Suppose the time until failure (in years) of a laptop computer follows an exponential distribution with a mean life of 6 years. a) What is the median life of a laptop computer (in years)? b) What is the probability that a laptop computer will last more than 6 years?
7. Suppose that waiting time, Y, at a particular restaurant follows an Exponential distribution with mean X, where X is a Geometric random variable with mean 1/ p. Find the unconditional mean and variance of Y.
The checkout time of a supermarket cashier follows an exponential distribu- tion, and the mean checkout time is three minutes. (a) What is the probability that a checkout time exceeds 2 minutes? (b) If 10 of these checkout times are selected, what is the probability that at most 3 checkout times that is less than 2 minutes?
Suppose 3 TAs will grade the final exam. Assume they are named Tı, T2, T3. The time it takes each of them to grade an exam is an exponential random variable, but with different parameters: the TA Ti grades the exams at a rate oft exams an hour Assume that the time to grade any exam is independent of the time to grade the other exams. Each exam is assigned to a uniformly random TA (a) (5 points) If X...
Suppose a worker needs to process 200 items. The time to process each item is exponentially distributed with a mean of 1 minutes, and the processing times are independent. Approximately, what is the probability that the worker finishes in less than 5 hours?
The time between arrivals of buses follows an exponential distribution with a mean of 60 minutes. a. What is the probability that exactly four buses arrive during the next 2 hours? b. What is the probability that no buses arrive during the next two hours? c. What is the probability that at least 2 buses arrive during the next 2 hours? d. A bus has just arrived. What is the probability that the next bus arrives in the next 30-90...
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds (a) Sketch this exponential probability distribution(b) What is the probability that the arrival time between vehicles is 12 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 6 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 32 or more seconds between...