# Solved – Is the value of a probability density function for a given input a point, a range, or both

This post says

A PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value.

Is it true?

this is the PDF of the standard normal distribution.

$$varphi(x) = frac{1}{sqrt{2pi}} e^{-x^2/2}$$

plug in x=0 into the formula above, I can get the probability of taking on one value.

Does that post mean the PDF could be used both for point and interval?

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The citation is true. When you plug $$x=0$$ to the PDF function, you do NOT get the probability of taking this particular value. The resulting number is probability density which is not a probability. The probability of taking exactly $$x=0$$ is zero (consider the infinite number of similarly-likely values in the tiny interval $$xin[0,10^{-100}]$$).
To further convince yourself that this $$varphi(x)$$ cannot be a probability, consider decreasing the standard deviation of your normal distribution from $$sigma = 1$$ to $$sigma = frac{1}{100}$$. Now, $$varphi(0)=frac{100}{sqrt{2pi}}$$ – much more than one. Not a probability.