How should I interpret this notation?

Question

I am reading some lecture notes and I'm not sure how to interpret this: $$ b_j(x)=p(x\mid s_j)=N(x;\mu,\sigma^2)$$ It is clear from the context that $N$ refers to normal distribution, but what exactly is $N(x;\mu,\sigma^2)$? Does it denote normal CDF?

Answer 1

i would interpret it as the normal density function. does it make sense for you?

Answer 2

Remember that the normal distribution is parametrized by its mean and variance which are usually denoted by $\mu$ and $\sigma^2$, respectively. The notation $f(x;\theta) $ generally means $ f $ is a function of $ x $ parametrized by $\theta $. $ N $ is referring to the normal density function.