Why is density function written as probabilty? Random variable confusion Related question: What is the meaning of pyx theta and px theta and px yz
In this question, doesn't the p represent the density function? Then why is it written in a lot of text as probability? For example, $p(y^i|x^i;\theta)$ is written as probability of $y^i$ given $x^i$ parametrized by theta, though it should be probability density of $y^i$ given $x^i$ parametrized by $\theta$.
As asked in comment -


It’s not. As already said in the comments $p$ is not reserved in mathematics for a probability, as any other letter or symbol isn’t. The meaning would follow from context. It is often used for probability density as in your example.
The quote says that $p$ stands for “distribution”, that’s imprecise. Distribution can be described by a probability mass function (discrete), probability density function (continuous), or cumulative distribution function. Later they use the word “probability” but they do it loosely. Obviously, the discussed function is a Gaussian probability density function, so it’s rather probability densities. It’s imprecise, but you would see people often saying “probability” when they mean “probability density”.
