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 exam within 3 hours?
Suppose the time it takes Alex to do this exam is exponentially distributed with parameter 3...
Two turtles are racing. The length of time that turtle A takes is expo 2 exponentially distributed with mean 5 minutes. The length that turtle B take is also exponentially distributed but with mean 7 minutes. Assume tha their times are independent. (a) What is the probability that A wins? (b) What is the probability that the winner takes longer than 6 minutes (c) What is the expected time of the winner? (d) What is the probability of a tie?
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 random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 29 minutes, what is the probability that X is less than 37 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 24 minutes, what is the probability that X is less than 29 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 25 minutes, what is the probability that X is less than 31 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 21 minutes, what is the probability that X is less than 26 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 22 minutes, what is the probability that X is less than 25 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5.What's the probability that a repair takes less than 5 hours? AND what's the conditional probability that a repair takes at least 11 hours, given that it takes more than 8 hours?
3. Two turtles are racing. The length of time that turtle A takes is expo 2 nentially distributed with mean 5 minutes. The length that turtle B take is also exponentially distributed but with mean 7 minutes. Assume tha their times are independent. (a) What is the probability that A wins? (b) What is the probability that the winner takes longer than 6 minutes (c) What is the expected time of the winner? (d) What is the probability of a...
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.8, i.e., mean = 1/lambda. What is (a) the probability that a repair takes less than 77 hours?