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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
- Two archers will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a). These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1). What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?Two sharpshooters will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a). These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1). What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?Everyday, James reverses his car from his driveway on to the road in such a way that there is a very small probability P that his car will be involved in a collision. ( i) Show that the probability that there will be no collision in a five-day week is (1−P)^5 and state one assumption that is made in your answer. (iii) Let P = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that James will avoid a collision in 500 days.
- A hexagonal cell within a seven-cell system has a radius of 1.425 km. A total of 119 channels are used within the entire system. If the load per user is 0.028 Erlangs, and λ = 1 call/hour, compute the following for an Erlang C system (chart is attached) that has a 7% probability of delayed call: B) What is the probability that a delayed call will have to wait for more than 9 sec?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?A hexagonal cell within a seven-cell system has a radius of 1.425 km. A total of 119 channels are used within the entire system. If the load per user is 0.028 Erlangs, and λ = 1 call/hour, compute the following for an Erlang C system (chart is attached) that has a 7% probability of delayed call: C) What is the probability that a call will be delayed for more than 9 sec?
- Let i_t denote the effective annual return achieved on an equity fund achieved between time (t -1) and time t. Annual log-returns on the fund, denoted by In(1 + i_t) , are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and o = 14%.An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%. Using only formulas, no tablesSuppose that the length of time spent by a student with a professor during office hours in minutes is an exponential r.v. with parameter ?=1/10. This professor only sees students in the office hour one at a time. Thus, if you arrive to the office and there is someone inside, you have to wait. Consider 5 randomly chosen days in which you visit the professor's office during the office hour period and someone arrives immediately ahead of you. What is the probability that in one of those days you will have to wait between 10 and 20 minutes?A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?
