Suppose we have independent and identically distributed observations y = (y,..., yn), with yi Exponential (A)....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose we have independent and identically distributed observations y = (y₁,..., yn), with yi Exponential (A). (a) Suppose that we specify ~ Gamma(a, ß) as the prior distribution on the unknown model parameter, A. Derive the posterior mean, E(Xly) and posterior standard deviation, Var(\ly). (5 points) (b) Now, suppose that we are interesting in learning about = 1, i.e., the mean of an Exponential (X) distribution. Show that a conjugate prior distribution for is an Inverse-Gamma (a, 6) distribution. You may use that if X Inverse-Gamma (a, ß), then the associated probability density function is Ba p(x|a, ß) = r(a)(¹/x)ª+¹exp(-8/x), defined over the range/support x > 0, with parameters a > 0 and 3 > 0. (5 points) Suppose we have independent and identically distributed observations y = (y₁,..., yn), with yi Exponential (A). (a) Suppose that we specify ~ Gamma(a, ß) as the prior distribution on the unknown model parameter, A. Derive the posterior mean, E(Xly) and posterior standard deviation, Var(\ly). (5 points) (b) Now, suppose that we are interesting in learning about = 1, i.e., the mean of an Exponential (X) distribution. Show that a conjugate prior distribution for is an Inverse-Gamma (a, 6) distribution. You may use that if X Inverse-Gamma (a, ß), then the associated probability density function is Ba p(x|a, ß) = r(a)(¹/x)ª+¹exp(-8/x), defined over the range/support x > 0, with parameters a > 0 and 3 > 0. (5 points)
Expert Answer:
Answer rating: 100% (QA)
4 Ramim sample from XN Gamma p prin Likelihons 2 Pid ... View the full answer
Related Book For
Probability And Statistics For Engineering And The Sciences
ISBN: 9781305251809
9th Edition
Authors: Jay L. Devore
Posted Date:
Students also viewed these mathematics questions
-
Suppose that observations X1, X2,..., Xn are made on a process at times 1, 2,..., n. On the basis of this data, we wish to test H0: the Xi's constitute an independent and identically distributed...
-
If X and Y are independent and identically distributed with mean and variance 2 , find E[(X Y) 2 ]
-
What is the price of a bond with a $10,000 face value, a 6.5% coupon rate with semi-annual coupons, and three years to maturity if it has a yield to maturity of 8%? OA. $9,606.84 O E. $11,310.53 O D....
-
Assuming 10% minimum required reserve ratio, 5% excess reserve ratio, and people holding 10% of cash received at home (not deposited in the banks), the money multiplier is equal to Select one: a....
-
The index of refraction of a glass rod is 1.48 at T = 20.0C and varies linearly with temperature, with a coefficient of 2.50 x l0-5/Co. The coefficient oflinear expansion of the glass is 5.00 x...
-
Presented here are the amounts of Assets, Liabilities, Stockholders Equity, Revenues, and Expenses of The Better Body, Inc., at December 31, 2010. The items are listed in alphabetical order. The...
-
Explain the following terms and their relevance to debt-finance decision makers: (a) Negative covenant. (b) Conversion premium. (c) Collateral. (d) Strip bonds. (e) Sukuk.
-
Using the information provided in BE4-2, prepare a condensed multiple-step income statement for Brisky Corporation.
-
Define and explain with example the project costs for supply chain management projects
-
Find the capacitor voltage for t 0 for each of the circuits in Fig. 7.107. (a) (b) 3 2 12 v ( .) 4V 412 S F 6 A
-
An urn has one blue ball and one red ball. Andy draws a ball from the urn randomly, observes the color of the drawn ball, and puts the ball back in the urn. He repeats until he sees the blue ball...
-
Diagnosis lab test and differential diagnosis treatment with medication and it's name and uses of scleroderma
-
Simplify. (3+9)0 (3+9)=
-
Sunn Company manufactures a single product that sells for $180 per unit and whose variable costs are $135 per unit. The company's annual fixed costs are $562,500. (1) Prepare a contribution margin...
-
Merger Company has 10 employees, each of whom earns $1,350 per month and has been employed since January 1. FICA Social Security taxes are 6.2% of the first $137,700 paid to each employee, and FICA...
-
Westerville Company reported the following results from last year's operations: Sales Variable expenses Contribution margin Fixed expenses Net operating income. Average operating assets $ 1,600,000...
-
Examine the five - component careers chart and choose the row that seems most relevant to your interests and abilities. Describe a job in each component column of that row. If you are uncertain,...
-
A. Select a recent issue (paper or online) of Report on Business Magazine, Canadian Business Magazine (online only), Bloomberg Businessweek, Fast Company, The Economist, or another business magazine....
-
What conclusion would be appropriate for an uppertailed chi-squared test in each of the following situations? a. a = .05, df = 4, x2 = 12.25 b. a = .01, df = 3, x2 = 8.54 c. a = .10, df = 2, x2 =...
-
The Centers for Disease Control and Prevention reported in 2012 that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD). a. If a random sample of 200 American...
-
The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses in Perth, Australia ("An Application of Bayes Methodology to the Analysis of Diary...
-
Prove that if \(G\) is an undirected tree with more than one vertex, then \(G\) contains at least two vertices of degree 1 .
-
The graph below shows computer links between an official vote-tallying center at vertex 1 and several precincts. For the sake of secrecy, links can be made secure, but since this is an expensive...
-
Finish the proof of Theorem 1, that is, if \(G\) is a connected graph with \(n\) vertices and \(n-1\) edges, then \(G\) is a tree.
Study smarter with the SolutionInn App