# Let X Continuous Random Variable With PDF

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## Let X Continuous Random Variable With PDF

A random variable X is called continuous if it satisfies P(X = x) = 0 for each x. 1 Informally, this means that X assumes a “continuum” of values. By contrast, a discrete random variable is one that has a finite or countably infinite set of possible values x with P(X = x) > 0 for each of these values.

If X is a continuous random variable and Y=g(X) is a function of X, then Y itself is a random variable. Thus, we should be able to find the CDF and PDF of Y. It is usually more straightforward to start from the CDF and then to find the PDF by taking the derivative of the CDF.

Note that before differentiating the CDF, we should check that the CDF is continuous. As we will see later, the function of a continuous random variable might be a non-continuous random variable.

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