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T distribution mathematical expectation
Hello, I have read your question elsewhere, too. Let me answer you:

Let me try to answer your question. I haven't studied MATLAB, but this problem can be solved by EXCEL (and programming):

1) Why is it a number of 3?

This is because the T distribution of non-standardized students has three parameters. That is to say, T-distribution can be extended to three-parameter position-proportion family (non-standardized student T-distribution), introducing position parameters and proportion parameters. You can Google it to learn more.

The relationship between nonstandard student T distribution and standard T distribution (with only one parameter) is the same as that between standard normal N(0, 1) and general normal N(mu, sigma^2), where mu is the position parameter and sigma is the scale parameter.

2) What is the number of 3? What is 1.0e+003 *?

According to your number 108, the estimated value of MLE (calculated by EXCEL and SOLVER) is:

Mu (position parameter) = 2243.3, Sigma (scale parameter) = 9 17.4, DF (degree of freedom) =7. 17.

It's just that the value of your three numbers has expanded 1000 times. So that 1.0e+003 * means "Please take the following value × 1000 as the estimated parameter value".

3) At the same time, remind: I checked with chi-square, and it seems that your 108 data "very" does not conform to the T distribution (of three parameters), so you can reject the assumption that 108 data conforms to the T distribution with 99.9% confidence. I drew a graph and found that the distribution of your 108 data seems to have two humps (one near 1400 and the other near 2700). Generally speaking, a lot of your data are concentrated around 1400 and 2700, while the data meeting the t distribution will be concentrated on the mathematical expectation (that is, mu, that is, 2243). The two humps can't be t-distributed. You can have a look again.