# Lost in the introduction discussing probability/likelihood [duplicate]

I have some questions about the following paragraph which introduces a masters level course.

In this unit we consider the Frequentist (i.e. counting) approach to statistical inference and computing the probability/likelihood of the data $$y$$ given the parameters $$\theta$$, $$P(y|\theta)$$. Under this approach we use Maximum Likelihood Estimation (MLE) to estimate the parameters of probabilistic/likelihood models, i.e. $$\hat{\theta} = > arg max_{\theta}P(y|\theta)$$. If we are dealing with a known probability distribution of the data then we use $$P(y|\theta)$$, but in general we are interested in the probability $$P(y|x, u, \theta)$$ where $$u$$ can be 'predictor' variables and $$x=x(u,\theta)$$ can be intermediate variables dependent on $$u$$ and $$\theta$$. In this unit we primarily focus on the cases of $$P(y|\theta)$$ and $$P(y|u=x, \theta)=P(y|x, \theta)$$.

Q1) I understand that big P means a discrete distribution. Does this statement only apply to discrete distributions?

Q2) Why is it talking about likelihood of data? I understood likelihood to pertain to parameters as in MLE?

I think big P in this notation is just for probability in general. That is, $$P(y|\theta)$$ is just probability of y given $$\theta$$.
Likelihood is used to refer to the likelihood function, which is the same in form as the probability density/mass function, but with the parameters as the unknown. Thus, while we can have $$f(x|\theta)$$ as the density/mass function of $$X$$ given $$\theta$$ value of parameters, we can have the corresponding likelihood function $$L(\theta|x)$$, where we are interested in $$\theta$$ and have the dataset $$x$$ to use.