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Relation between frequency spectrum and PDF of a random variable

Relation between frequency spectrum and PDF of a random variable
  1. What is the PDF of the random variable?
  2. What is spectrum in probability distribution?
  3. How does probability and random variable related to each other?

What is the PDF of the random variable?

The probability density function or PDF of a continuous random variable gives the relative likelihood of any outcome in a continuum occurring. Unlike the case of discrete random variables, for a continuous random variable any single outcome has probability zero of occurring.

What is spectrum in probability distribution?

The power spectrum of a time series. describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range.

How does probability and random variable related to each other?

The probability distribution for a random variable describes how the probabilities are distributed over the values of the random variable. For a discrete random variable, x, the probability distribution is defined by a probability mass function, denoted by f(x).

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