Let us consider the exponential distribution with density function f(y|0) = 0e-y and ani.i.d. sample Y; ~Exponential (0) for i = 1, ..., n.a) Show that a gamma prior distribution is conjugate for 0.b) Calculate the posterior mean and variance under this conjugate prior.c) For the following data0.4, 0.0, 0.2, 0.1, 2.1, 0.1, 0.9, 2.4, 0.1, 0.2use the exponential distribution and(i)(ii)Plot the posterior distribution for gamma prior parameters a = B = 0.001.Perform sensitivity analysis for various values of a and b. Produce related plotsdepicting changes on the posterior mean and variance.

“Since you have posted a question with multiple sub-parts, we will solve the first sub-parts for…

Answered: Let us consider the exponential…

Let us consider the exponential distribution with density function f(y|0) = 0e-y and an i.i.d. sample Y; ~Exponential (0) for i = 1,..., n. a) Show that a gamma prior distribution is conjugate for 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: To evaluate if auditors might be helped in determining the chances of fraud if they carefully…

A: This question is about testing the difference between two sample means to determine whether a…

Q: An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses…

A: From the given information we have Sample mean (x̅1) = 76.7Sample mean (x̅2) = 77.5Sample size (n1)…

Q: A major difference between grounded theory and other research methods is its specific approach to…

A: Grounded theory is a research method that has a specific approach to theoretical development.

Q: Pls do fast within 5 minutes and i will give like for sure Solution must be in typed form The demand…

A: Calculating elascity, E(p)=(-p)*f'(p)f(p)f'(p)=-(2/3)*pE(p)=2*p2(256-p2)

Q: Exercise 3. Let X be a random variable with mean and variance o2. For a ER, consider the expectation…

A: Given information: The random variable is X. The mean of X is μ. The variance of X is σ2. The term a…

Q: Exercise 1. Using classical statistics describe the structure of monthly turnover of 80 shops [in…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer 1 question at a…

Q: Select the proper interpretation of a confidence interval for a mean at a confidence level of C%. a…

A: To find: To Select the proper interpretation of a confidence interval for a mean at a confidence…

Q: The following data are taken from a study conducted by the National Park System on the temperatures…

A: To find: Inter Quartile Range (IQR)

Q: The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution…

A: The objective is to construct a frequency distribution based on the given limits and check whether…

Q: Consider the following causal diagram:

A: Direct casual effects are nothing but there exists a direct path from one variable to another…

Q: NT #4 Permutations and Combinations Set up the following, do not calculate a) Finding the number of…

A: The permutation is used to list when the order of data is important. The combination is used to list…

Q: To produce enough energy from your own wind turbine, the site’s annual average wind speed should…

A: Given Information: Sample size n=1114 Sample mean x¯=8.019 Sample standard deviation s=3.813

Q: Is there evidence tjattje average infant mortality rate increases with teen birth rate? (Assume…

A: From the regression output, the parameter estimates is given as: Term Estimate Std Error…

Q: what would the critical value for this question be?

A: The sample size for first sample is 39, and second sample is 39.

Q: Friskie is having her fifth litter. The prior litters have either been three normal pups or two…

Q: Moose are over-browsing aspen such that regeneration is greatly reduced. Fencing has been used but…

A: This question seeks to design an experiment to test the effectiveness of more expensive fencing for…

Q: 9. It is known from past experience that in a certain plant, there are on the average 4 industrial…

A: 9. Given The data is as follows: Avg. industrial accidents per year, λ=4 accidents/year

Q: Looking at the frequency table. What determines the column totals? Explain what makes the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Consider a dataset {x}_1 with mean and standard deviation s. Assume that two new datasets, {y}_₁…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer 1 question at a…

Q: 10. The boxplot shown below results from the heights (cm) of males listed in a data set. What do the…

A: As per our guidelines we are suppose to answer only one question kindly post the remaining question…

Q: Consider the experiment of tossing a coin twice and then rolling a dice a. Develop a tree diagram…

A: Note: Since you have posted multiple subparts questions, we are answering first three subparts for…

Q: How do you calculate the coefficient of determination (R^2) in a simple linear regression model?

A: Introduction :The coefficient of determination, denoted by R^2, is a statistical measure used in…

Q: The table below displays the results of a study investigating the effectiveness of bicycle safety…

A: Answer:- Given data , Using formula, Relative risk = {a/(a+b)}/{c/(c+d)}, where a= head injury…

Q: A sample of n = 6 scores has a mean of M = 10. If one score with a value of X = 12 is removed from…

A: Given that A sample of n = 6 scores has a mean of M = 10

Q: A new vaccine was tested to see if it could prevent the ear infections that many infants suffer…

Q: 2. In the early 1900s, an effort was made to protect the deer population that lived on the Kaibab…

A: This graph shows the population changes of deer living on the Kaibab Plateau in Arizona from 1905 to…

Q: According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015…

A: Given The data is as follows: The mean is 78.1 years. The pop. sd is 15 years. CL=0.95

Q: A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for $50,…

A: Given data in the problem is $5-->55% $50-->20% $100-->15% $1000-->10% Odds of a…

Q: 1. Income distribution in the population: We look at income x (measured in millions) in a…

A: The data is given as- Midpoint:x Frequency:f cummulative (0.0,0.1] 0.05 289 289 (0.1,0.2]…

Q: 45 56 67 78 89 100 Class Limits -55 66 77 88 > > > > > > ||||| 99 110 44.5 55.5 66.5 77.5 88.5 99.5…

A: Obtained data table:

Q: Hello, When I sum up the variance, I'm getting 2.75. And not 1.65. Also, how did you get the…

A: Given The data The Expected value is calculated as EX=3.06

Q: The following table shows the percentage of high school men and women who enrolled in college within…

A: Given information: x M W 0 54% 37.90% 5 57.30% 45.30% 10 55.20% 48.50% 15 52.60% 49.50%…

Q: A recent survey of the NHL found that the number of goals scored in Hockey *BY A PLAYER* in an 82…

A: Given that: Population mean, μ=42 Population standard deviation, σ=8 Sample size, n=23

Q: Given are five observations for two variables, x and y. (Round your answers to two decimal places.)…

A: Given information: The values for x and y are given.

Q: In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal…

A: given dataN = 5000normal distributionμ = 45 mphσ = 14 mph

Q: The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large…

A: Given that: Sample size, n=25 Sample mean, x¯=9450 Sample standard deviation, s=1956

Q: and use your results to compare the funds with respect to risk. Which fund is and Fund 3 is

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

Q: Consider all of a class companies with a similar probability of default. Assume that the probability…

A: Given : Total number of companies expected to default: n=3

Q: A random sample of 42 chemists from Washington state shows an average salary of $46283, the…

A: The question is about hypo. testing Given : Randomly selected no. of chemists from "WS" ( n1 ) = 42…

Q: d. Find the IQR. The IQR for the test scores is 32.5. (Round to one decimal place as needed.) e.…

A: we have to find variance of scores X :…

Q: 2. Consider a dataset {x}=1 with mean and standard deviation s. Assume that two datasets, {y}_₁ and…

A: Note: Hi, there! "Since you have posted a question with multiple-subparts, we are answering first…

Q: The table shows some information about the weights, in grams, of some potatoes. Range 101 Lower…

A: 2) The range value is 101 and the maximum value is 185.

Q: Identify the lower class limits, upper class limits, class width, class midpoints, and class…

A: The question is about frequency distribution Given : To find : 1 ) Lower class lim. 2 ) Upper…

Q: Section 21 introduced important characteristics of data summarized by the acronym CVDOT. What…

A: Introduction A graph is a good way to visualize data.

Q: bability below. X ≤ 100) 1-F(99) None of the above. F(99) 1-F(100) F(101) - F(100) F(101) F(100) -…

A: X is a discrete random variable. We have to determine which one is correct choice.

Q: What is the predicted suicide rate per 100000 people ?

Q: Let X~ N₂(μ, E), p≥ 2. Let (ui, Ai) (1 ≤ i ≤p) be the ith eigenvector-eigenvalue pair of Σ. Let Z,…

A: Solution: From the given information, Let (ui , λi) (1≤i≤p) be the ith eigenvector-eigen value pair…

Q: Describe how each of the following variables can be measured using the nominal, ordinal and ratio…

A: A variable can either be measured as numbers or not. If it is measured with numbers it is called a…

Q: *In the 1800s, a man with dwarfism who lived in Utah produced a large number of descendants: 22…

A: Given information: The data for 15 families with 1 parent had dwarfism is given.

Question

Let us consider the exponential distribution with density function f(y|0) = 0e-y and an
i.i.d. sample Y; ~Exponential (0) for i = 1, ..., n.
a) Show that a gamma prior distribution is conjugate for 0.
b) Calculate the posterior mean and variance under this conjugate prior.
c) For the following data
0.4, 0.0, 0.2, 0.1, 2.1, 0.1, 0.9, 2.4, 0.1, 0.2
use the exponential distribution and
(i)
(ii)
Plot the posterior distribution for gamma prior parameters a = B = 0.001.
Perform sensitivity analysis for various values of a and b. Produce related plots
depicting changes on the posterior mean and variance.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Question C

Let us consider the exponential distribution with density function ƒ(y|0) = 0e¯ºy and an
i.i.d. sample Y₁ ~Exponential (0) for i = 1, ..., n.
a) Show that a gamma prior distribution is conjugate for 0.
b)
Calculate the posterior mean and variance under this conjugate prior.
c) For the following data
0.4, 0.0, 0.2, 0.1, 2.1, 0.1, 0.9, 2.4, 0.1, 0.2
use the exponential distribution and
(i)
(ii)
Plot the posterior distribution for gamma prior parameters a = В
Perform sensitivity analysis for various values of a and b. Produce related plots
depicting changes on the posterior mean and variance.
= 0.001.

Solution

by Bartleby Expert

SEE SOLUTION

Follow-up Question

question b and c

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

A civil engineer is studying the live loads on a highway bridge. Let Y and Z denote the live load (in ten thousands of pounds) for traffic going east and west, respectively, at a randomly selected time of day. Suppose these random variables have a joint distribution with density function f(y,z) = (1/400)yz2e–y/5–z/2, for y > 0, z > 0. What type of distributions do Y and Z have? Use this to confirm the mean and standard deviation of each variable.
On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
Consider the functionf(x)=1/x, defined on the interval 1≤ x≤ e describe the shape of distribution after graphing the density function.
A type of network router has a bandwidth total to first hardware failure called ? expressed in terabytes. The random variable ? is modeled by a distribution whose density is given by one of the following functions: fs(s) = 1/? for s [0,?] with a single parameter ?. Consider the bandwidth total to failure ? of the sequence of the two routers of the same type (one being brought up automatically when the first is broken).Express ? in terms of the bandwidth total to failure of single routers ?1 and ?2. Formulate realistic assumptions about these random variables. Calculate the density function of the variable ?. Given an experiment with the dual-router-system yielding a sample ?1 , ?2 , ..., ?? , calculate the likelihood function for ?. Propose a transformation of this likelihood function whose maximum is the same and can be computed easily. An actual experiment is performed, the infrastructure team has obtained the bandwidth totals to failure given by the sequence ?10 of numbers (225, 22,…
Let Y be a random variable whose density function is 3y2 ? y3? f(y|θ)= θ3 exp −θ3 , y>0,where θ > 0 is a parameter. Using an appropriate pivotal quantity, verify that?Y,Y? (− log α)1/3 (− log(1 − α))1/3is a confidence interval for θ with coverage probability 1 − 2α.
Let the continuous random variable X denote the current measured in a thin copper wire in milliamperes. Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?
What is the probability density function (pdf) of a continuous random variable W with cumulative distribution function (CDF) given by F(w) = w^2, 0 < w < 1?
Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that W takes on a value between 0.5 and 1.75? What is E(W)? Suppose that the domain of W changes to 0<t<2.5, what happens to the Probability Density Function (PDF)?
please use the density of X. Find PDF of exp distribution and then plug it into E(e^tX).
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.