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- 11 the probability distribution of discete random variable x is given by p (X=x) = k÷ x+1 for x = 1,2,3 a) find the value of K where K is constant b) compute P(x=2) C) compute p(x=2 or x=3)You are an aerospace engineers designing the next generation of space shuttles that includes two engines —one active, the other in reserve. If the primary engines fails, the second is automatically brought on line. Suppose a typical mission is expected to require that engine to work at most 5000 hours. According to the manufacturer's specifications, engine are expected to fail once every 10000 hours. What are the chances that such engine system would not remain functioning for the full 5000 hours? Hint, Use Gamma Distribution.Amedical researcher says that less than 79% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 75% think that healthy children should be required to be vaccinated. At a= 0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below SE (a) Identify the claim and state H, and H,. ome Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) ents O A. Less than % of adults in the country think that healthy children should be required to be vaccinated. ok O B. More than % of adults in the country think that healthy children should be required to be vaccinated. Contents C. %% of adults in the country think that healthy children should be required to be vaccinated. O D. The percentage of adults in the country who think that healthy children should be…
- A botanist suspects thatdue to the different light and atmospherical conditions of the two rooms in their lab, plants willhave different developmental characteristics. To test this, two identical seeds of tomato plant are selected and potted separately. One pot stayed in Room 1, and the other in Room 2. The botanist tracked the development of the plants(in numbersof leaves grown)for a 5-month period and found that the plantinRoom 1 grew leaves much quicker than the plant in Room 2. However at the end of the period, both plants had similar amounts of leaves grown. a.Identify the predictor and predicted variables. b.Determine if the studyisexperimental or non-experimental, explain why. c.Describe the levels of measurement for the variables, explain why.6.A golfer practices different parts of their game for hours. Specifically, the golfer practices:(1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each partof their game is exponentially distributed. If the golfer is practicing their putting, they will alwaysswitch to their short game after an average of 30 minutes. When the golfer practices their short game,they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to theiriron game with probability 0.4. When they practice their iron game, they do so for an average of 60minutes. After practicing their iron game, the golfer will switch to putting or to their short game withequal probability.(a) Draw the CTMC rate diagram, clearly label your states and transition rates (qij ’s)(b) Find the transition rates out of the states (vi’s) and transition probabilities (Pij ’s).(c) Find the limiting probabilities (make sure to write out the balance equations).(d) In the long…
- The Collector’s Choice Inc. (CCI), a luxury car import company, has an old warehouse at the Port of Miami, Florida, where it temporarily stores expensive sports cars and automotive parts that arrive from Europe. This summer, CCI has noticed that the termite infestation in the warehouse has escalated to a point where tenting cannot be postponed anymore. (Tenting is the process of wrapping a building inside a huge tent that is subsequently filled with a poisonous gas capable of killing most forms of life inside, including insects, plants, pets, and human beings.) CCI’s pest control company’s contract specifies a to-do list of pre-tenting tasks, which include: Turning off all air-conditioning units and opening all windows of the warehouse Turning off all internal and external lights, including those operating on a timer Pruning all outdoor vegetation at least 18" away from the warehouse Soaking the soil around the warehouse on the first day of tenting The requirement of opening all…Consider an investor borrowing at the risk free rate and investing a share of his wealth greater than one in the market portfolio. The beta of this investor’s portfolio is Equal to one Smaller than one Larger than one Equal to zeroAn ecologist is studying the impacts of air pollution on giant panda populations, specifically on panda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close to the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : i. 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 1 in 3 female baby pandas…
- #14).Environment-friendly agricultural practice includes the application of pesticides when it is really necessary, e.g., at the beginning of a pest emergence. Such practice, depending on the field conditions, and the reaction of growers, for the same level of “alert”, inspired this question.Assume that in the middle of the growing season in a given area, there is one pest emergence every two weeks on average. There is a generalized emergence of pests in a given area. At this stage of the emergence, not all growers decide to apply pesticides, hoping that the emergence will be brief or without implication for their field. Accordingly, assume 75% of the growers in that area at that time decide to apply pesticides. a) What is the probability that among five growers randomly sampled, two decide not to apply pesticides? b) What is the probability that among 10 randomly sampled growers, more than nine decide to apply pesticides?