5 b)From part (a) now suppose that we observe a sample of size ten with zi = 21. Let the prior be specified10with parameters a = 1 and 3 = 4. Find an estimate for the parameter A using the squared error loss L(6, a) =(0- a). Give your answer to two decimal places.Hint: If X - Gamma(a, 3) then E(X) = a3.Question Threea)Let X1,...., X be ii.d. Poisson(A) and let A have a Gamma(a, 8) distribution with density of the form,f(z,a, 3) =1-le /T(a)3"the conjugate family for the Poisson. Find the posterior distribution for A.Gammaa+) X; + 1.nB +1GammaX.n8 +1a+Gammaa+>x1n3 +1Gammaa+n8 +1)(a+x:Gamma1n3 +1 Please complete and neat solved and optionnumber marked thanks

Answered: Image /qna-images/answer/da0efbb2-74a7-45a1-986d-75aa21b76c99.jpg

Answered: b) From part (a) now suppose that we…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
using the z table (table e), find the critical value (or values) for each. a. alpha=0.10, two tailed test b. alpha=0.01, right tailed test c. aplha=0.005, left tailed test
f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
The random variable X has a Bernoulli distribution with parameter p. A random sampleX1, X2, . . . , Xn of size n is taken of X. Show that the sample proportionX1 + X2 + · · · + Xnnis a minimum variance unbiased estimator of p.Given that X1, X2, . . . , Xn forms a random sample of size n from a geometric population withparameter p, show thatY =n∑j=1
a. Use the 2nd-order Runge-Kutta Method to approximate y(t) with h= 0.25 b. Use the 4th-order Runge-Kutta Method to approximate y(t) with h=0.25 c. Plot both sets {yi} obtained in (1) and (2) d. Determine the eventual population level (as t→∞) reached from initial population.
A researcher is interested in testing whether annual house hold income in Philadelphia is normal. So she took a sample of 50 house holds and found that skewness (s)= 2.3190 and Kurtosis (k) = 6.7322. Use the Jarque- Bera Test to test , at alpha 0.05, whether income follows normal distribution. -Yes, population is normal because Chi-Square test is higher than critical value. -Yes, population is normal because Chi-Square test is less than critical value. -No, population is not normal because Chi-Square test is higher than critical value. -No, population is not normal because Chi-Square test is less than critical value.
1.19 Suppose x1, . . . , xn is a sample from the process xt = µ + wt − .8wt−1,where wt ∼ wn(0, σ2w).(a) Show that mean function is E(xt) = µ.(b) Use (1.33) to calculate the standard error of ¯x for estimating µ.(c) Compare (b) to the case where xt is white noise and show that (b) issmaller. Explain the result.1.20 (a) Simulate a series of n = 500 Gaussian white noise observations as inExample 1.8 and compute the sample ACF, ρb(h), to lag 20. Compare thesample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.19.](b) Repeat part (a) using only n = 50. How does changing n affect the results?1.21 (a) Simulate a series of n = 500 moving average observations as in Example 1.9 and compute the sample ACF, ρb(h), to lag 20. Compare thesample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.20.](b) Repeat part (a) using only n = 50. How does changing n affect the results need solution for 1.21
In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
QUESTION 23 Assuming all other factors are held constant, if the df value for a two-tailed t-test with α = .05 were increased from df = 6 to df = 20, what would happen to the critical values for t? a. The critical values would further from t = 0. b. The critical values would not change. c. The critical values would move closer to t = 0. d. This is impossible to determine without more information.
To this point, the work of days missed per month by workers at a large corporation has average 2.25. A new flexible workday arrangement has been introduced and it is hoped that by introducing this "flex time" that the average workdays miss per month will be reduced. Let alpha=.05 A) defined the appropriate parameter for this problem and then set up the appropriate Null and alternative hypothesis a. The average number of work days missed by all workers at a large corporation. Ho: x bar=2.25; Ha: x bar < 2.25 b. The average number of work days missed by all workers at a large corporation Ho: mu = 2.25; Ha: mu < 2.25 c. The number of work days missed by the workers d. The average number of workdays mess by the 20 workers at a large corporation. Ho: mu =2.25; Ha: mu. 2.25

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