3.1 Repeat observing a distance for n times with independent equal weight. Please proof that the most probable value of the observations is direct mean by the Least Square Method. Also calculate the standard deviation of the MPV.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need detailed explanation to solve this exercise from Adjustment Theory. I have no clue how to solve it.

 

3.1 Repeat observing a distance for n times with independent equal
weight. Please proof that the most probable value of the observations is
direct mean by the Least Square Method. Also calculate the standard
deviation of the MPV.
Transcribed Image Text:3.1 Repeat observing a distance for n times with independent equal weight. Please proof that the most probable value of the observations is direct mean by the Least Square Method. Also calculate the standard deviation of the MPV.
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Step 1: Overview

To prove that the most probable value (MPV) of the observations is the direct mean by the Least Square Method, we can use the principle of least squares. The goal is to minimize the sum of the squares of the differences between each observation and the MPV. Let's denote the observations as x1, x2, ..., xn.

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