Problem 4: Consider the Rayleigh distribution with parameters 0 and 01: 1 F(t) = 1 - exp(-0₁t-20₁t²) a) Find the hazard function (failure rate) for F. b) For what values of 0₁ does F have positive failure rate? Negative rate? Constant rate?
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Enter the estimated y-value When analyzing the model y; = Bo + B1 * Xi + & where & E N(H,o) we got I Bo = (3.886, 7.102) and Ie1 = (2.666,4.562). Enter an estimate of y when x = 3 with at least 2 decimal places accuracyGiven the two h-scatterplots below, would you say the data is spatially autocorrelated in the direction chosen? Why? h 10 m h 20 m 10 10 024 10 20 NP
- 17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. CountI am not sure how to complete the incorrect section of this problem.- (Sec. 6.1) Using a long rod that has length µ (unknown), you are going to lay out a square plot in which the length of each side is µ. Thus the area of the plot will be µ². However, because you do not know the value of µ, you decide to make n independent measurements X1,...,X, of the length. Assume that each X; has mean µ and variance o². (a) Show that X² is not an unbiased estimator for the area of the square plot µ². [Hint: for any rv Y, E[Y²] = V[Y] + E[Y]². Apply this for Y = X.] (b) For what value of k is the estimator X² – kS² unbiased for µ²?
- 1(1) Let X = b(16,- find E(4-3x) and distribution function.= 1. (Review) (a) Suppose that X ~ Cauchya and c> 0. Show that Y cX Cauchyca (Hint: This is change of variable problem. First find the cdf for Y, then find the pdf by differentiating) (b) If X₁, ..., Xn are i.i.d. and X; ~ Cauchya, then Sn~ Cauchya (The point: Unlike in the various versions of the law of large numbers, Sn does not converge to a constant in any sense).
- 1) 1-sample t-test is used to compare a sample to a theoretical average Calculate t-score: t-score=(sample average - theoretical average)/SEM of the sample. Take the absolute value of it (make it positive) if needed. In order to calculate the p-value, type into excel: =tdist(t-score, df, tails) Value: 1 Tidal Volume (it is 7ml/kg of body mass in average) represents the air volume moved during regular breathing into and out of the lungs. During the lab, students collected measures 6.8, 6.9, 7.0, 7.1, 7.3, 7.6, 6.8 ml/kg. The collected data indicate that the students attending this lab had average tidal volumes. True False Check AnswerIn a certain dynamic measurement application the input(x) – output(y) relationship is given by y=1+(1+x)e-x With what uncertainty must x be determined to yield a relative uncertainty of ±2 percent for y at a value of x = 3,8?Numerical analysis. Urgent
