Verify that the above is a valid density function. A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. With the current quality of the process, what is the percentage of batches that are not acceptable?
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- In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by p(t)=ae−0.119t where t is the time in seconds and a is a constant.Find the constant a.Nitrite is commonly determined by a colorimetric procedure using a reaction called the Griess reaction. In this reaction, the sample containing nitrite is reacted with sulfanilimide and N-(1-Napthyl) ethylenediamine to form a colored species that absorbs at 550 nm. Using an utomated flow analysis instrument, the following results were obtained for standard solutions of nitrite and for a sample containing an unknown amount:Solution Absorbance at 550 nm2.00 μM 0.0656.00 μM 0.20510.00 μM 0.33814.00 μM 0.47418.00 μM 0.598Unknown 0.402(a) Find the slope, intercept, and standard deviation of the calibration curve.(b) Construct the calibration curve.(c) Determine the concentration of nitrite in the sample.A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is f(x)= {kx2O < x < 2} 0 otherwise a. Find the value of k and draw the corresponding density curve.[ Hint: Total area under the graph of f (x) is 1.] b. What is the probability that the lecture ends within 1min of the end of the hour? c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour?
- we investigate if a period of time feels longer or shorter when people are bored compacted to when they are not bored. using independent samples, we obtain these estimates of the time period (in minutes) sample 1 (bored) xbar= 14.5 s2x= 10.22 n= 28 sample 2(not bored) xbar=9.0 s2x=14.6 n=34 (a) what are Ho and Ha? (b) compute t-obt (c) with alpha =.05, what is t-crit?Find the area under the given curve over the indicated interval. y= e2x ; [0,4]For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
- Suppose the amount of time (x) to complete an exam is uniform between 30 and 60 minutes. A) Draw the density curve for for the unknown height (h) B) What is the probability that the exam takes between 30 and 35 minutes or 55 and 60 minutes? Enter your answer as a fraction.Log(price)=9.5 +0.6*log(sqm_land)+0.17*rooms-0.04*log(CO2) N=900 R2=0.52 Question 1 Assume a CO2 level of 3 and a land area of 400square meters. How much is the price of the house going to increase if we extend it from 2 to 3 rooms? Question 2 Calculate the degrees of freedom associated with these estimates.Is this high enough for standard normal critical values to be applied?I was calculating a conditional density function and I got an answer of 2x+3y all over 2x+3/2. When I checked the answer, it was 4x+6y all over 4x+3. Those two answers are the same, but my question is--is there some protocol as far as what is proper form to express an answer in when dealing with density functions?
- Given the area in the first quadrant bounded by y² = 4x and x = 4. Find the first moment with respect to the x-axis of the area. 2 8 4 16Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. Given that 33.6% of all possible observations of the variable exceed 8, determine the area under the density curve that lies to the a. right of 8. b. left of 8.Consider the following 10 measurements about the cohesion of a soil: 12 kPa, 14 kPa, 15 kPa, 14.5 kPa, 16.0 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa. Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively. (1) Draw the PDF of the cohesion; (2) Evaluate the probability that the cohesion based on the PDF is less than 5 kPa, 10 kPa, and 15 kPa; (3) Assess the effect of the type of distribution on the results.