The Law of the Unconscious Statistician states that if you have a random variable and you apply a function to it, you can find the expected value of the transformed variable by integrating the product of that function and the probability density function of the original variable. This principle allows us to calculate expectations for functions of random variables without needing to directly compute probabilities for the transformed variable. It connects to understanding moments and variances of random variables, distributions of functions, and how transformations impact random variables.
congrats on reading the definition of Law of the Unconscious Statistician. now let's actually learn it.