Theoretical Distributions
- We have reality, but we want the truth from that (inference)
- Notation
- English/Latin letters: data
- Modifications of English/Latin letters: calculations with real data
- Greek letters: truth
- Modifications of Greek letters: our estimation of the truth; most commonly: hat So \(\hat{\mu}\) is “my estimate of what I think 𝜇 is.”
- Theoretical distribution generated data.
- Don’t care about mean in our data, but about the mean of the true distribution for everyone
- And the bigger our number of observations gets, the gooder-enougher we become.
- Hypothesis testing: we can check if our distribution has a certain mu, by checking out our standard deviation and then running a two-sided t-test.