4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.

4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

4)
A set of measurements is given as follows.
X = [0.1, 0.3, 0.8, 12,4, 7,9]
We want to approximate the source of this data with Gamma distribution, i.e.,
X~Gamma(a, B).
For Gamma distribution, the mean and variance can be found from the below
equations.
a
Hx
a
o =
Find the parameters of Gamma distribution to fit the data. Come up with two other
distributions that you think are good representation of this data. Justify your answer.

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For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is p = 1 - 7.2 where p is the minimum percentage of scores that fall within k standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.1 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.1 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 96 percent of the scores? Note: To answer part c you will need to solve the equation for k.
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