The question presents us with a pdf for the continuous random variable X, which represents the height of students (18 years old). "It is estimated that X possesses the probability density function of:
f(x) = 348x-x^2-29700/18432 for 150<x<198"
I have confirmed that the estimated pdf is, in fact, a pdf as the integral between 150 and 198 is equal to 1. I also found the estimated value (=174) and the variance (=115.2) by using their respective formulae.
The next part of the question is to "evaluate the accuracy of this estimated model by using a suitable emprirical test to evaluate the model." I have collected the following data:
From the data it is already evident that the heights recorded fall outside of the given domain of (150<x<198) from the estimated model.Would the next step be to compare the average height from the data to the expected value given by the estimated pdf? (pdf gives 174 vs 184.3 from the data set). I am a bit stuck at the moment and any guidance would be great!
The next part of the question is to use the data collected to construct a pdf of my own to represent X. I haven't approached this problem either so if someone could point me in the right direction it would be greatly appreciated.
f(x) = 348x-x^2-29700/18432 for 150<x<198"
I have confirmed that the estimated pdf is, in fact, a pdf as the integral between 150 and 198 is equal to 1. I also found the estimated value (=174) and the variance (=115.2) by using their respective formulae.
The next part of the question is to "evaluate the accuracy of this estimated model by using a suitable emprirical test to evaluate the model." I have collected the following data:
186 | 178 | 198 | 172 | 179 | 181 |
188 | 196 | 181 | 189 | 183 | 191 |
183 | 201 | 170 | 187 | 187 | 175 |
186 | 190 | 180 | 189 | 186 | 175 |
175 | 187 |
From the data it is already evident that the heights recorded fall outside of the given domain of (150<x<198) from the estimated model.Would the next step be to compare the average height from the data to the expected value given by the estimated pdf? (pdf gives 174 vs 184.3 from the data set). I am a bit stuck at the moment and any guidance would be great!
The next part of the question is to use the data collected to construct a pdf of my own to represent X. I haven't approached this problem either so if someone could point me in the right direction it would be greatly appreciated.