A renewal process has a renewal function M (t) = 4t + (1-e-4t). (a) What is the mean inter-event time? (number) (b) What is the expected time until the next event (from the beginning of the process) at time t = 3 ? (number)
Q: A poll was taken every month on how voters will vote on the next federal election. Here are the…
A: Given that , a poll was taken every month on how voters will vote on the next federal election. Let…
Q: Prediction intervals are not sensitive to th normality assumption because Xn+1 is a future…
A: The prediction interval measures the predicted valued of dependent variable such that 95% of times…
Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have…
A: Let the random variable X be the white blood cell count per cubic millimetre of whole blood in a…
Q: 4. For Poisson arrivals at à packets sec, if packet size is fixed as K bits, link rate is R bps: a.…
A: @solution::: Transmission rate=RCurrently transmitted packet = × bitsWaiting queue=n packets…
Q: A fisherman puts out his net in the evening and empties it the following morning. During the night,…
A:
Q: A 5 year endowment assurance contract provides a death benefit of €15,000 at the end of the policy…
A: The chance of occurrence of observation in the sample or event with equal likelihood to all the…
Q: Derive the probability of ultimate extinction of a branching process.
A: One of the most significant approach in branching process is calculating the probability of eventual…
Q: The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and B with…
A: Introduction to Poisson distribution: A random variable X is said to have a Poisson distribution…
Q: At a train station, the time between trains leaving the station follows an Exponential distribution…
A: The probability distribution function of exponential distribution is given by f(X)=λe-λx; x>0,…
Q: Example 8: Thẻ average value x of a random sample of observations from a certain population is…
A:
Q: 1. A fund is established for the benefit of 500 workers all age 35 with independent future life-…
A: GivenThe initial fund balance =FAll employees are of age 35, so number of years for them to be 65…
Q: The time intervals between successive barges passing a certain point on a busy waterway have an…
A:
Q: The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and B with…
A: Solution: Poisson distribution: A random variable X is said to have a poisson distribution with a…
Q: 8)- In a Technometrics, May 1985 article, Vardeman and Ray suggest that the number of industrial…
A:
Q: Losses follow a Pareto distribution with parameters alpha= 2, theta =1000 For a coverage with…
A:
Q: he life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential…
A: Given The life of low grade lightbulbs follow an exponential distribution with mean 0.5 yearsλ=10.5…
Q: 4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew…
A: As per the questionLet T be the time between two successive replacementsIt is given by the sum of…
Q: Prove that - 1. The waiting time for a Poisson distribution is Exponentially distributed. i.e. For a…
A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…
Q: (See image for introduction) What p-value for a test of H0: λ= 2 is associated with an observation…
A:
Q: A diagnostic test for a certain disease is applied to n individuals known to not have the disease.…
A:
Q: One of the two teller machines handles withdrawals only while the other handles deposits only in a…
A:
Q: Wilat is oper end point in a 98% prediction interval for the 5-year rate of return? Coefficients…
A: Solution
Q: The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and B with…
A:
Q: 1. The Poisson distribution is often used to describe how many times an event takes place within a…
A: Maximum likelihood estimation represents one of the most important approaches to estimation in all…
Q: The number of requests for assistance received by a towing service is a poisson process with rate α…
A: the number of requests received follows a Poisson distribution with parameter 2 per hour. We can say…
Q: 3. Obtain the moment generating function of the binomial distribution. Derive from it the result…
A:
Q: Prove that - 1. The waiting time for a Poisson distribution is Exponentially distributed. i.e. For a…
A: Let the probability of k arrivals in a unit of time is P(k) modelled by Poisson and probability of…
Q: A portfolio's value increases by 20% during a financial boom and by 7% during normal times. It…
A: We have given that A portfolio's value increases by 20% during a financial boom and by 7% during…
Q: Two dice are rolled together six times. The random variable of interest, Y , is the number of times…
A: The term probability means the chance of occurrence of an event. The probability value ranges…
Q: A life insurance company sells whole-life assurance policies with a sum assured of $20,000, payable…
A: Given Sum assured=20000 Premium=420 payable annually in advance and the variance of the present…
Q: fetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and B with expected…
A: Given: The lifetime of a bulb is modeled as a Poisson variable. The expected lifetimes of bulb A =…
Q: The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential…
A: Please see below
Q: 0.5 for A mortality table is defined such that¸p¸ ={1— x100. Calculate the complete expectation of…
A: Answer is 40.
Q: 3. A production facility has two stages in tandem, with no waiting room in between. Scrvice times at…
A: @solution:::
Q: Kolmogorov's law of fragmentation states that the size of an individual particle in a large…
A:
Q: Univariate time series models are especially useful when it comes to forecasting. Consider the…
A: Given that, MA1 process 0.5ut-1+ut and ut-1=0.2 and ut=-0.8
Q: Example 1.14 If X is independent random variable having exponential distribution with the parameter…
A:
Q: Time headway in traffic flow is the elapsed time between the time that one car finishes passing a…
A: Solution
Q: The time intervals between successive barges passing a certain point on a busy waterway have an…
A:
Q: A grasshopper hops between three flowers, labelled 1, 2, 3. It starts from flower 1. Once it arrives…
A: Given: A grasshopper hops is labelled 1, 2, 3. It starts from flower 1. Once it arrives at a flower,…
Q: The time intervals between successive particle arrivals at a counter generate an ordinary renewal…
A: GivenThe time intervals between successive particle arrivals at a counter. After 10 particles the…
Q: The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential…
A: The probability mass function and CDF of exponential is given as f(x)=λe-λx x≥0F(X)=1-e-λx…
Q: Exponential distribution can be used to represent a series of k stations that must be passed through…
A: True
Q: An electrical system consists of 2 components (C1 and C2) functioning independently and are set in a…
A: Note: Hey there! Thank you for the question. As you have posted a question with more than 3…
Q: The time intervals between successive barges passing a certain point on a busy waterway have an…
A:
Q: At a car factory, two jobs are performed at the specified costs given in the table. Each job can be…
A: Given table : JOB SPEED DAILY COST THE PROBABILITY OF COMPLETION IN 2 DAYS THE PROBABILITY OF…
Q: ind the expected total illumination time (in years), given you do exactly 3 bulb re- placements 2.…
A: Given: The expected lifetime of A =0.25 The expected lifetime of B =0.5 When a bulb’s life ends,…
Q: Find the expected value of the yearly rate of return of an investment that, for an initial cost of…
A: The formula for the annual rate of return is : Annual return=Ending valueInitial value1/no. of…
Q: In finance, one example of a derivative is a financial asset whose value is determined (derived)…
A: Disclaimer : “Since you have posted a question with multiple sub-parts, we will solve first three…
Step by step
Solved in 2 steps
- Epidemic Model In a population of 200,000 people, 40,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune cannot become infected again. Of the people who are infected, 5 will die each year and the other will recover. Of the people who have never been infected, 25 will become infected each year. How many people will be infected in 4 years?The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .Consider a linear birth–death process where the individual birth rate is λ=1, the individual death rate is μ= 3, and there is constant immigration into the population according to a Poisson process with rate α. Please explain and show work! (a) State the rate diagram and the generator. (b) Suppose that there are 10 individuals in the population. What is the probability that the population size increases to 11 before it decreases to 9? (c) Suppose that α = 1 and that the population just became extinct. What is the expected time until it becomes extinct again? α in Greek letter alpha.
- The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and B with expected lifetime 0.25 years and 0.5 years, respectively. When a bulb’s life ends, it stops working. You start with new bulb of type A at the start of the year. When it stops working, you replace it with a bulb of type B. When it breaks, you replace with a type A bulb, then a type B bulb, and so on. 1. Find the expected total illumination time (in years), given you do exactly 3 bulb replacements. 2. Your replacements are now probabilistic. If your current bulb breaks, you replace it with a bulb of type A with probability p, and with type B with probability (1 – p). Find the expected total illumination time (in years), given you do exactly nn bulb replacements, and start with bulb of type A. Answer for part 2 exists in closed form in terms of n and p.Lost-time accidents occur in a company at a mean rate of 0.3 per day. What is the probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3? Assume Poisson situation. P(X=3)At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the total weight of seeds accumulated by a nest is exponentially distributed with parameter λ = 1/5, (a) What is the probability that the total combined weight of the seeds gathered by 100 nests will be larger than 4 95 pounds by the end of next summer? (b) What is the probability that the average weight of the seeds gathered by the 100 nests is larger than 5.3 ? (c) What assumptions are you making to answer parts (a) and (b)? Do you think those assumptions make sense in the context of this problem? Explain. (d) Tell us about the possibility that the total combined weight of the seeds gathered by 2 nests follows a normal distribution. Justify your answer in the specific context of this problem (ants, nests, seed-gathering). That is, do not just make generic statements that you think apply to every context in the world.
- The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs typesA and B with expected lifetime 0.25 years and 0.5 years, respectively. When abulb’s life ends, it stops working. You start with new bulb of type A at the start ofthe year. When it stops working, you replace it with a bulb of type B. When itbreaks, you replace with a type A bulb, then a type B bulb, and so on. 1. Find the expected total illumination time (in years), given you do exactly 3bulb replacements.2. Your replacements are now probabilistic. If your current bulb breaks, youreplace it with a bulb of type A with probability pp, and with type B withprobability (1 – pp). Find the expected total illumination time (in years),given you do exactly nn bulb replacements, and start with bulb of type A.Answer for part 2 exists in closed form in terms of n and p.An enzyme reversibly binds a substrate. The rate constant (kcat) for catalytic conversion of enzyme-substrate complex into product and free enzyme is 1.0 s-1. The rate constant for dissociation of enzyme-substrate complex (k-1) is 9.0s^-1. 1) For each substrate binding event, what is the probability that substrate is converted into product rather than dissociated without conversion? 2) What is the probability that 20 consecutive binding events result in no product formation? 3) If you evaluated 1,000 different sets of 20 consecutive binding events, what would be the average number of product molecules formed (per 20 binding events)? 4) What is the probability that 20 consecutive binding events result in a number of product molecules at least equal to this average?A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are plotted on a normal probability plot. The points approximately follow a straight line. True or false: a) X1, …, Xn come from a population that is approximately lognormal. b) X1, …, Xn come from a population that is approximately normal. c) ln X1, …, ln Xn come from a population that is approximately lognormal. d) ln X1, …, ln Xn come from a population that is approximately normal.
- Old Faithful is a geyser located in Yellowstone National Park in Wyoming, USA. Millions of travelers come from afar to witness Old Faithful's eruptions each year. The data provided show the waiting time until the next eruption for 272272 Old Faithful eruptions in 1990. Suppose that prior to 1990, travelers to Yellowstone are told that Old Faithful is expected to erupt, on average, every 6969 minutes, and park scientists believe that this average is no longer true. Suppose that, based on historical data available over several decades, the scientists are comfortable assuming that all eruption waiting times have a known standard deviation of 17.24817.248 minutes. 54 74 62 85 55 88 85 51 85 54 84 78 47 83 52 62 84 52 79 51 47 78 69 74 83 55 76 78 79 73 77 66 80 74 52 48 80 59 90 80 58 84 58 73 83 64 53 82 59 75 90 54 80 54 83 71 64 77 81 59 84 48 82 60…2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.2. You are to wait for the first car to arrive at an inspection station. It is believed that the waittime (in minutes) follows an Exponential distribution with parameter ✓ = 10 minutes. a. You are to wait for 10 independent cars to arrive (cars arrive one by one to the station, thinkof X i as the time for the i-th car). How long do you expect to wait to complete this task? Howmuch do you expect the true wait time to vary around the expected time?
