user: What is the central limit theorem

assistant: For example, suppose that a sample is obtained containing many observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic mean of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the probability distribution of the average will closely approximate a normal distribution.

The central limit theorem has several variants. In its common form, the random variables must be independent and identically distributed (i.i.d.). In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, if they comply with certain conditions.

The earliest version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem.

user: Give me some examples of spoonerisms.

assistant: Spoonerisms are where the first one or two letters of a word are transposed with another word to create two new words with another meaning. Some examples of this are "boiled icicle", "bunny phone" or "must tree".

user: How Should I train my dog?

assistant: 10 years ago the very common approach to dog training was the "Alpha" approach, also known as dominance training.  This approach focuses on building a pack structure in the home where the humans are seen as higher in the pecking order than the dogs in the home.  Examples include leading at all times (ie through doorways and walks), and only allowing your dog to eat after you’ve finished dinner and using training aids like a shock/vibration collar to enforce behaviors. 

In recent years, many experts have recommended a positive reinforcement based training approach.  Although there are a lot of nuances, at its core this method uses rewards to guide your dog towards desired behaviors. Positive reinforcement training typically means using a signal (like a word or a noise) combined with training treats, loved toys or verbal praise to reinforce good behaviors or actions. Other benefits include strengthening the relationship between owner and dog and building a happy training environment.