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A random variable $X$ is called continuous if its set of possible values is uncountable, and the chance that it takes any particular value is zero ($\text{P}(X = x) = 0$ for every real number $x$). A random variable is continuous if and only if its cumulative probability distribution function is a continuous function.

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How can $N(x|\mu, \sigma^2)$ not be 0?

How can $N(x|\mu,\sigma^2)$ not be 0? Because a Gaussian distribution is continuous and therefore there are an infinite number of values that x can occupy in the Gaussian distribution therefore the p …
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