It is evident that the probability of a continuous random variable is always between an interval and is the area under the curve that the interval makes with the corresponding PDF. Then why in naive bayes we just directly take the probability from a PDF_gaussian without integrating in some interval as given in the assignment. It might come out to be greater than 1?. I will be grateful for the help. Thank you

In continuous PDF you can calculate the probability P(X=x). You know the pdf of a gaussian distribution pdf. So you can calculate it. The area under the curve between a and b gives the probability P(a<X<b).

But as in the lectures the probability P(X=x) i.e the probability of continuous random variable X at a point x is zero

Yes you are right. There should be a mistake since pdfs give the probability at a given point.It doesnβt give zero. Maybe a mentor explains it better.

How may I find a mentor here?

So, as i progressed on the course I got to know in the 3rd week that this is not actually the probability rather a likelihood that we have to maximize. This leads us to the gaussian distribution with mean and variance calculated from the samples which maximizes the likelihood.