et X1, X2, ..., X10 be a random sample from a gamma distribution with α = 3 and β = 1/θ. Suppose we believe that theta follows a gamma-distribution with α = 28 and β = 17 and suppose we have a trial (X1 , ... , Xn ) with an observed x̄ = 28.2 What is the posterior distribution of θ What is the Bayes point estimate of θ associated with the square-error loss function?

et X1, X2, ..., X10 be a random sample from a gamma distribution with α = 3 and β = 1/θ. Suppose we believe that theta follows a gamma-distribution with α = 28 and β = 17 and suppose we have a trial (X1 , ... , Xn ) with an observed x̄ = 28.2 What is the posterior distribution of θ What is the Bayes point estimate of θ associated with the square-error loss function?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

See similar textbooks

Related questions

Q: If the probability density of a random variable is given by 0 < x < 1 1<x<2 elsewhere X f(x) = {2-x…

Q: sample has a mean of 72. Assume the population standard deviation is 11.3. What is the 99%…

A: Let be the population mean number of chocolate chips per cookie for big chip cookies.Given…

Q: A building sells for $325,000 and a 30% down payment is made. A 20-year mortgage at 4% is obtained.…

A: Here, given that the building sells for $325,000 and a 30% down payment is made.Then, we have to…

Q: The shelf life of a high-speed photographic film is being investigated by the manufac turer. The…

A: Number of…

Q: at is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. at is the…

A: is given that, Regression equation is,a. We know that,F-statistics is,Decision: , we reject…

Q: The mean value of land and buildings per acre from a sample of farms is $1300, with a standard…

A: Here, we given that the value of mean and standard deviation for the given case .Then, we have to…

Q: Compute R2 (to 3 decimals). Compute Ra2 (to 3 decimals). How good is the fit provided by the…

A: The regression has 4 independent variables.Given:The regression equation is,

Q: A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.5 years.…

A: The question is about normal distribution Given :Population mean lifetime of a dishwasher ( ) = 12…

Q: water due on the mortgage is larger than the value of the home). There are 160 homes in the…

A: It is given that Probability, p = 35% = 0.35Sample size, n = 160

Q: ~NORM(800,50). What value of X corresponds to Z= 0.76?

A: Answer Given X~ NORM [800, 50]Mean =800standard deviation =50Z = 0.76

Q: (a) What is the probability that the cost will be more than $430? (Round your answer to four decimal…

A: Automobile repair costs continue to rise with the average cost now at $367 per repair. Assume that…

Q: Suppose that 4% of the 2 million high school students who take the SAT each year receive special…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Problem 15-8 Spreadsheet Problem: Seasonal and Trend Estimated Sales (LG15-2)

A: you can follow these steps:Define the historical monthly sales data. Create a NumPy array with the…

Q: b. Employee records for the Sentin indicate that 18% of employees are college graduates. The…

A: 18% of employees are college graduates.There are 5498 employees nationwide.Event A: The first…

Q: Assuming that the population is half male and half female, what is the probability that a random…

A: Given :Assuming that the population is half male and half female So , the population proportion of…

Q: Babies born weighing 2500 grams (about 5.5 pounds) or less are called low-birth-weight babies, and…

A: The data is defined below as follows: It is clear that,Let X denotes the birth weight for children…

Q: a.exactly 3 of them weigh more than 82 gram (Answer 4 decimal place) b) at least one potato is more…

A: Let X be the weight of the stall potatoes are normally, distributed with mea,n 85 gram and standard…

Q: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of…

A: On-time:P=0.801-P =0.20_________________________________late:P =0.201-P =0.80

Q: For many years businesses have struggled with the rising cost of health care. But recently, the…

A: n= 400 Sample size Sample proportion

Q: The annual number of visits to a health care provider can be modeled by a discrete random variable…

A: (As per our standard guidelines, we are supposed to answer only 3 sub-parts.)A. The probability that…

Q: The 90% confidence interval is (). (Round to two decimal places as needed.) The 95% confidence…

A: It is given that Sample mean = 83.83Population standard deviation = 14.13Sample size = 65

Q: It is reported that Americans stayed an average of 6.5 nights when they went on vacation. A student…

A: a)Suppose µ is the population average nights American stayed when they went on vacation.

Q: Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is…

Q: a. What value of c is needed to ensure that the joint pdf is valid? 14 b. What is the probability…

Q: Identify the sampling technique used. At a local community college, five statistics classes are…

A: In simple random sampling procedure, each of the population unit has same chance of being included…

Q: A study was performed to determine the percentage of people who wear life vests while out on the…

A: From the provided information,

Q: A regression equation is given by y 11.37395 +2.82773x. The following information about the variable…

A: The regression line is Also, We have to find

Q: In game craps, a round ends when either the selected number or a 7 comes up. So, the player rolls…

A: This is Geometric distribution

Q: A simple random sample with n= 53 provided a sample mean of 27.5 and a sample standard deviation of…

A: Sample size n =53Sample mean=27.5Sample standard deviation =4.4NOTE:- According to bartleby…

Q: Final assembly note before packaging. The results appear below. Brand P Q Total 376 131 507 NUMBER…

A: Number of correctionsBrand123TotalP3765417447Q131166153Total5077023600

Q: A regression equation is given by y=11.37395+2.82773x.The following information about the variable x…

A: A regression equation is given by y=11.37395+2.82773x.The following information about the variable x…

Q: Assume X has a binomial distribution. Use the binomial formula, tables, or technology to calculate…

A: (a)The probability of P(3≤.x≤6).is obtained below as follows:Let X denotes the random variable which…

Q: ownership varies across age groups. Suppose that the estimated percentage of people who own at least…

Q: actorial experiment involving two levels of factor A and three levels of factor B resulted in the…

A: A factorial experiment involving two factor and three levels which is given in tabular form Factor…

Q: fP(En F) = 0.192, P(EF) = 0.32, and P(FE) = 0.4, then (a) P(E)= (b) P(F) = (c) P(EUF) = - 9.

A: P(E ∩ F)=0.192P(E|F)=0.32P(F|E)=0.4

Q: A random variable X is normally distributed. It has a mean of 229 and a standard deviation of 23.…

A: It is given that the random variable X is normally distributed with mena 229 and standard deviaton…

Q: ed that the water temperature in Hays County is 72 degrees Fahrenheit year round, which is…

A: It is known that the water temperature in Hays County is 22.2 degrees Celsius.The objective is to…

Q: A research wants to determine if pre-natal exposure to the hormones in birth control pills alters…

A: The researcher exposes a group of pregnant midshipman fish to birth control hormones and records the…

Q: Since the z score for the winner of Best Actor is z = and the z score for the winner of Best Actress…

A: Actor=X , Actress=YX=35 , Mean=43.6 , Standard deviation=6.7Y=48 , Mean=36.7 , Standard…

Q: toss a coin three times. Let X be the number of observed heads. a. Determine the pmf of X. b. Find…

A: A coin is tossed 3 times then the sample,space of the outcome S={HHH, HHT, HTH, THH, THT, HTT, TTH,…

Q: What is a Markov matrix

A: A Markov matrix, also known as a stochastic matrix or a transition matrix, is a square matrix used…

Q: A research wants to determine if pre-natal exposure to the hormones in birth control pills alters…

A: The researcher exposes a group of pregnant midshipman fish to birth control hormones and records the…

Q: The data in the accompanying table give the weights (ing) of randomly selected quarters that were…

A: The image is so blurred that it is hardly readable. The candidate is advised to see whether the…

Q: Find the best predicted value of y (height) given an adult female with an arm circumference of 40cm

A: Regression equation of y on xwhere= change in y when there is a unit change in x= estimate of y when…

Q: Joe wondered what the average age of a Netflix Outer Banks viewer is, so he conducted an SRS of 12…

A: The question is about hypothesis testingGiven :Randomly selected no. of subscribers ( n ) = 12Sample…

Q: This is a practice test. I would like to know how to solve using excel or megastat The following…

A: SalaryERAJ Santana162.38C. Lee12.5T. Lincecum0.42.21C. Sabathia62R. Halladay52.12J. Peavy5.42.75D.…

Q: Using the table provided, interpret the adjusted R squares. iii) Explain F-Change with Significance…

A: ii) It is stated that the adjusted R square is 0.630. The adjusted R square, which takes into…

Q: If 10% of a population of products is defective, what is the probability of randomly selecting 100…

A: P = 0.10 q = 1-0.10 = 0.90N = 100

Q: The table shows the CBR and CDR of Y Province. Compute for: 1. Time to reach 50,000,000 population…

A: The question asks to calculate the year when the population of Y Province reaches 50 million, and…

Q: 1) For each of the data sets below, indicate which type of graph you would choose to display the…

Question

Let X1, X2, ..., X10 be a random sample from a gamma distribution with α = 3 and β = 1/θ. Suppose we believe that theta follows a gamma-distribution with α = 28 and β = 17 and suppose we have a trial (X1 , ... , Xn ) with an observed x̄ = 28.2

What is the posterior distribution of θ
What is the Bayes point estimate of θ associated with the square-error loss function?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution