Probability calculation of a normally distributed continuous variable
I see a formula to calculate the probability for any value(x=x1) in the image attached. Don't the probability of any continuous variable for a particular values would be zero? Because probability is the area right? which is computed between 2 values. So, don't the probability be 0 for any particular continuous value? Please someone correct me if i am wrong!
You are correct. The probability for any particular value in a continuous distribution is zero. The equation you've posted isn't a formula for the probability, it's a formula for the Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there are an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer that, in any particular draw of the random variable, how much more likely it is that the random variable would equal one sample compared to the other sample.
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