Coursera course on probabilities - for data science, actually quite good in explaining a lot of the basic tools,prob, conditional, distributions, sampling, CI, hypothesis, etc.
I.e, Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.
The problems considered by probability and statistics are inverse to each other.
In probability theory we consider some underlying process which has some randomness or uncertainty modeled by random variables, and we figure out what happens.
=> Underlying process + randomness and random variables -> what happens next?
In statistics we observe something that has happened, and try to figure out what underlying process would explain those observations.
=> observe what happened -> what is the underlying process?
Finally, probability theory is mainly concerned with the deductive part, statistics with the inductive part of modeling processes with uncertainty
Std vs variance - std is in the same metric as the mean, is the root of variance., allows outliers to influence, will not result in samples cancelling each other without the square root in the formula.
what are the known facts? Inherent in both probability and statistics is a population,
every individual we are interested in studying, and a sample, consisting of the individuals that are selected from the population.
in probability: would start with us knowing everything about the composition of a population, and then would ask, “What is the likelihood that a selection, or sample, from the population, has certain characteristics?”
In statistics: we have no knowledge about the types of socks in the drawer. we infer properties about the population on the basis of a random sample.