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- When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands isexponentially distributed with parameter 1 = 1/463.5. What is the probability that, on a randomoccasion when I go swimming, I swim at least 458.1 meters without getting hand cramp?Give your solution accurate to 4 decimal places.The entire human genome can be considered to a long book broken into pages. Suppose that the number ofmutations on a single page of this book has a Poisson distribution with parameter λ = 1/2 . For a given page, calculate that there are atleast 2 mutations on the page?Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?
- The expected life of a certain component in a mechanism is treated as a random variable having a gamma distribution with a = 3 and ß = 2. The average expected life of such component is 12 months, what is the probability that this component can have a greater than average expected life?cauliflower seeds germinate in 6 days or more. Find the standard deviation of times taken for germination for cauliflower seeds. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places. Suppose that the times taken for germination for cauliflower seeds are normally distributed with a mean of 7 days. Suppose also that exactly 80% of the O dayscertain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
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- Jobs arriving to a computer have been found to require CPU time that can be modelled by an exponential distribution with parameter 1/140 per millisecond. The CPU scheduling discipline is quantum-oriented so that jobs not completing within a quantum of 100 milliseconds will be routed back to the tail of the queue of waiting jobs. Find the probability that an arriving job will be forced to wait for a second quantum. Of the 800 jobs coming in during a day, how many are expected to finish within the first quantum.Three batteries with a life span of 1 day were used simultaneously for one day. Battery usage follows a uniform distribution and three batteries are used independently of each other. Find the PDF of the sum of the remaining three batteries after the day.The arrival of customers to a small local food restaurant may be modeled by a Poisson process with rate of 1 per 15 min period. Assume customer will only arrive if there is at least one customer present. Each customer on average stays for a time exponentially distributed with mean 20 minutes. This is modeled as a birth-death process. (i) Compute the probability that the capacity of 20 will be reached if we start with 5 customers.