


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...
Suppose the time it takes Alex to do this exam is exponentially distributed with parameter 3 per hour, and the time it takes Ben to do the exam is exponentially distributed with parameter 2 per hour. Assume that these two times are independent. (a) What is the probability that Alex finishes before Ben? (b) What is the expected time in minutes until the first one finishes this exam? (c) What is the probability that neither Alex nor Ben finishes the...
The time between arrivals at a toll booth follows an exponential distribution with a mean time between arrivals of 2 minutes. What is the probability that the time between two successive arrivals will be less than 3 minutes? What is the probability that the time will be between 3 and 1 minutes?
Suppose that the average amount of time a student studies for an exam follows a normal distribution with a mean of 6 hours with a standard deviation of 3.15 hours. What is the probability that a student studies less than 10 hours? A. 0.1020 B. 0.7525 C. -1.27 D. 0.8980
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...