Why density of gaussian can be used to compute probabilities?

In the lectures of week 1, professor estimates probabilities using p(x) which is the density of a gaussian random variable with median mu and variance sigma squared. Why that and not integrate over a small interval? What is the rationale?

Thanks in advance.

Though the instructor uses the word “probability”, the p(x) used in this lecture is actually the probability density for the gaussian distribution.

You are correct that an integral between two values would be required to compute the probability over that range.

I’ll submit a request to correct this issue in the lecture.

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