Let X Continuous Random Variable With PDF

PDF Name	Let X Continuous Random Variable With
No. of Pages	43
PDF Size	4.02 MB
Language	English
PDF Category	Education & Jobs
Source / Credits	stat.auckland.ac.nz
Uploaded By	Pradeep

Let X Continuous Random Variable With - Summary

A random variable X is defined as continuous if it meets the criteria P(X = x) = 0 for every value of x. This essentially means that X can take on a broad range of values, which is different from a discrete random variable that can only take finite or countably infinite specific values where P(X = x) > 0 for each of these instances.

Understanding Continuous Random Variables

When we say that X is a continuous random variable, it opens up a world of possibilities for associated random variables. For instance, if we have Y = g(X), where g is a function of X, then Y too is a random variable. This leads us to the important concepts of cumulative distribution function (CDF) and probability density function (PDF).

Finding PDF from CDF

Finding the PDF of Y is typically easier when we start with its CDF. To obtain the PDF, we simply take the derivative of the CDF. However, it’s crucial to ensure that the CDF is continuous before we proceed with differentiation. Remember, we might encounter situations where the function of a continuous random variable results in a non-continuous random variable.

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