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Method of Moments

The Method of Moments is a system used to estimate the parameters of an unobservable population by using sample moments. This is achieved by equating the sample values to the population values and solving for the required parameters. While this method is not used as widely anymore due to the Method of Maximum Likelihood being more useful, it still has some use because of it’s easier to calculate equations. It is also used as a first approximation to the maximum likelihood in situations where the equations for maximum likelihood are too complicated to calculate. The method of moments also has a significant disadvantage when samples are small, where the calculations will give parameters that are nonsensical to the problem, often because it is unable to take into account all the all the relevant information for the sample.

 

Game Theory Question and Business Examples

1. Two major wireless phone companies are going to offer 4G services in the country of Uruguay. Because of county regulations each company can only offer a single plan. The companies can only offer one of three possible plans. One of the companies (South Wireless) contracted a market study to estimate the potential number of cu

Methods of Moments and Maximum Likelihood

9. (Method of Moments and Maximum Likelihood, 8 points) The exponential random variable is given by f(x) = lamba(e^-lamba(x)), x (greater or equal to) 0. a) Recall that EX = 1/lamba. Use the method of moments to estimate lamba. b) Find the maximum likelihood estimate of lamba.

Method of Moments Estimate

Method of Moment Estimate Given f(x)=xθ^x e^x 0≤x≤1 And the sample data {0.3, 0.4, 0.1, 0.6, 0.8, 0.9, 0.1, 0.4, 0.8, 0.9} What is the method of moments estimate of θ?

Method of Moments estimate of discrete data

Suppose that X is a discrete random variable with P(X=1) = θ and P(X=2)= 1- θ. Three independent observations of X are made: X1 = 1, X2 = 2, X3 = 2. Find the Method of Moments estimate of θ. Please show your work.

Moment generating function

What is the moment generating function of the probability density function f(x) = 4x-x^2 for 0<x<2? I know it has something to do with E(e^tx) in other words integrate over 2 to 0 e^tx (4x - x^2) dx, but I don't know how to do it. How do I use this to find the mean and variance of this distribution? (somebody mentioned Taylor