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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days. The area to the left of X = 245 is 0.0947. What is the probability that a randomly selected human pregnancy lastsSuppose 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 2per 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?
- You consider investing £800 in stocks of the company X for a certain period. There is a possibility for X to merge with Y, in which case you expect your investment to appreciate £300, otherwise you expect it to depreciate £200. Also, rather than investing, you can choose to keep your £800. By using a utility function U(x)=x−−√, and by defining pthe probability that X merges with Y, what is the condition that p must satisfy for your investment to be worthwhile (rounded to two decimal places)?When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands is exponentially distributed with parameter ?=1/313.3λ=1/313.3. What is the probability that, on a random occasion when I go swimming, I swim at least 593.3593.3 meters without getting hand cramp?Give your solution accurate to 4 decimal places.Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
- Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.The life (in years) of a certain type of electrical switch has an exponential distribution with an average lifetime of 2 years. For a single system, what is the probability we can keep the switching mechanism operable for 10 years if we assume we will have to replace a switch due to failures three times during the 10-year period?Suppose that you have ten lightbulbs, that the lifetime ofeach is independent of all the other lifetimes, and that eachlifetime has an exponential distribution with parameter l.a. What is the probability that all ten bulbs fail beforetime t?b. What is the probability that exactly k of the ten bulbsfail before time t?c. Suppose that nine of the bulbs have lifetimes that areexponentially distributed with parameter l and thatthe remaining bulb has a lifetime that is exponentiallydistributed with parameter u (it is made byanother manufacturer). What is the probability thatexactly five of the ten bulbs fail before time t?
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