0, if x < -3 2, f(x) = -4, if – 3 < x < –1 if – 1< x < 3 if x > 3 0, and 9(æ) = / f(t)dt -3 Determine the value of each of the following: A.) g(-4) = в) 9(-2) %— c.) g(0) = D.) g(4) E.) The absolute maximum of g(x) occurs when x = which makes g(x) = NOTE: It may be helpful to make a graph of f(x) when answering these questions.
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- A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next customFor b there are two cases and for c I have to plug the initial data into the odeIndividual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,...,6-6), what is the pmf of X (= the total number of times a die is rolled)? What are E(X) and V(X)?
- People having Raynauds syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 12 subjects with the syndrome, the average heat output was x = 0.64, and for n = 12 non-sufferers, the average output was 2.05. Let µ1 and µ2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with σ1 = 0.2 and σ2 = 0.2. 1) Consider testing H0: µ1 − µ2 = 0 versus Ha: µ1 − µ2 < 0 at level 0.01. Describe in words what Ha says, and then carry out the test. 2) What is the probability of a type II error when the actual difference between µ1 and µ2 is µ1 − µ2 = −1.2? 3) Assuming that m=n, what sample sizes are required to ensure that β=0.1when µ1− µ2 = −1.2?Which of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance oneThe revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the number of stores andS(t) is the average revenue per store per month. Couturereleases a statement to their investors saying that currently they have 50 stores with a total revenueof$7,500,000 and expect to increase the number of stores by about 2 stores per month and increasetotal revenue by about$250,000 per month. What does this statement imply about the current rateof change of the average revenue per store per month?
- As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decadeConsider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with pmf x 1 2 3 4 5 6 p(x) 1/5 2/15 3/15 4/15 3/15 2/15 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00.If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]
- f there is no seasonal effect on people getting sick, we would expect equal numbers of people getting sick in each season (winter, spring, summer and fall). A student takes a census of students who took Marketing Research in 2019 and finds that of the 280 students who took Marketing Research in 2019, 75 were sick in winter, 65 were sick in spring, 68 were sick in summer and 72 were sick in fall. She wonders if the excess in the winter is an indication that sickness rates are not uniform throughout the year. What is an appropriate H1? a. The number of people getting sick is not equally distributed across the four seasons. b. The observed values equal the observed values. c. The number of people getting sick is equally distributed across the four seasons. d. The expected values equal the expected values.Suppose Tank A has 30 gallons of water containing 55 oz (ounces) of dissolved salt, Tank B has 20 gallons of water containing 26 oz of dissolved salt and Tank C has 50 gallons of water without any salt. Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min. Water flows in and out of tank A, B and C are as follows: Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min.Water flows from Tank A to Tank B at a rate of 3 gal/min.Water flows from Tank B to Tank A at a rate of 1.5 gal/min.Water flows from Tank B to Tank C at a rate of 3.5 gal/min.Water flows from Tank C to Tank B at a rate of 1 gal/min.Water drains from Tank C at a rate of 1.5 gal/min. a) Sketch the diagram that describe the above system. b) Determine the concentration of the brine inside each tank. c) Write the mathematical model that describe the above system.The populations, P, of six towns at time t in years are given by(i) P=2,090(1.08)t(ii) P=560(1.12)t(iii) P=2,700(0.9)t(iv) P=1200(1.18)t(v) P=800(0.78)t(vi) P=2000(0.99)t (a) Which towns are growing in size? Which are shrinking? Select all that apply.Growing towns: (i) (ii) (iii) (iv) (v) (vi) Shrinking towns: (i) (ii) (iii) (iv) (v) (vi) (b) Which town is growing the fastest? What is the annual percent growth rate for that town?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is growing the fastest. It is growing at a rate of % per year. (c) Which town is shrinking the fastest? What is the annual percent decay rate for that town? Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is shrinking the fastest. It is shrinking at a rate of % per year. (d) Which town has the largest initial population (at t=0)? Which town has the smallest?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the largest…