Question: Suppose that you are to observe a single random variable X which has a Poisson distribution having a mean theta. The family of conjugate priors

Suppose that you are to observe a single random variable X which has a Poisson distribution having a mean theta.

The family of conjugate priors is the family of gamma distributions. Give the pdf of the number of this family so that the mean of the prior distribution is 100 and the variance of the prior distribution is 25.

Given an arbitrary observation x give the pdf of the posterior distribution and based on the single observed value x give the Bayes estimate based on the squared error loss function

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Please help with questions 1, and make sure codes work on R Studios. Consider a location (locus) in the genome of a diploid organism where two different versions (alleles) of the DNA exist in the...

Suppose that each of two statisticians A and B must estimate a certain parameter whose value is unknown ( > 0). Statistician A can observe the value of a random variable X, which has the gamma...

4) Maximum Likelihood Estimation (15 pts). Consider a random variable X (possibly a vector) whose distribution (density function or mass function) belongs to a parametric family. The density or mass...

Unit II Continuous Probability Distributions: The Normal Distribution Normal Dist1 Towards the Meaning of Continuous Probability Distribution Functions: When we introduced probabilities, we spoke of...

We will use the Minitab macro PoisGamP, or poisgamp function in R, to nd the posterior distribution of the Poisson probability when we have a random sample of observations from a Poisson( )...

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

file: simulate_python2.py from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt import numpy as np import random import sys def plot_gaussian(x,y,z,filename=None): """ Plot the...

Student: Sterling White Instructor: David Scott Date: 10/11/22 Course: Math 1324 PreCalculus for Business Assignment: Section 5.3 Homework 8. A manufacturing company makes two types of water skis. a...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Hi, I am in difficulty when I kept trying to do these R questions. Could you give me help to solve these R questions? Thank you so much. Note: R code and the code output required Part 1 A radioaCtive...

A 22.0 cm diameter coil consists of 20 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to plane of the coil, changes at a rare of 8.65 x 103 T/s Determine...

Q2 Consider the plate shown in Fig. 1. The plate is modelled using one square bilinear element and one three-noded linear triangular element. The temperature at the five nodes are denoted by T1, T2,...

Broca Corporation has a current ratio of 2 . 5 . Which of the following transactions will increase Broca's current ratio? Question 2 2 Select one: a . the purchase of inventory for cash. b . the...

Compute Payroll Floatin Away Company has three employees-a consultant, a computer programmer, and an administrator. The following payroll information is available for each employee: Consultant...