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The elite runners in an ultra-marathon will cross the finish line at random times described by a Poisson Process with rate λ=8 per hour. The 6th-place runner has just finished the race. We are interested in the time-lag from now until the 10th-place runner crosses the finish line. Consider the density function of this random time-lag. Calculate the parameter w: Calculate the height of f(x) at x-o: Calculate the Mode M: hours Calculate the height of f(x) at x-M: Calculate the probability that the time-lag exceeds 42 minutes: Calculate the probability that the time-lag is less than 60 minutes: Calculate the probability that the time-lag is between 36 minutes and 42 minutes: Calculate the probability that the time-lag is not between 18 minutes and 48 minutes: Calculate the median m Hint: In these questions, convert minutes into hours.) hours (Hint: Use trial-and-error.)

math   Statistics-And-Probability   
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Answer #1

calculate the parameter w=1.333

calculate the height of f(x) at x=0 2.22

mode=8hours

calculate the probability that the time lag excess 42 minutes=0.7 hours

calculate the probability that the leg is less than 60 minutes = 1

clculate the probabilty that the time is between 36 minutes and 42 minutes 0.5

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