PROBABILITY DENSITY FUNCTION PDF
In other words, the area under the pdf bounded by the specified values. The probability density function is non negative everywhere, and its integral over the entire space is equal to 1. Since for continuous distributions the probability at a single point is zero, this is often expressed in terms of an integral between two points. If the pdf is not constant over the range of interest, the multiplication becomes the integral of the pdf over that range. Probability Density Function For a continuous function, the probability density function (pdf) is the probability that the variate has the value x.
For example, the probability that the signal, at any given instant, will be between the values of 120 and 121 is: (121 - 120) × 0.03 = 0.03. To calculate a probability, the probability density is multiplied by a range of values. The chance that the signal happens to be exactly 120.50000 is very remote indeed! This is because there are an infinite number of possible values that the signal needs to divide its time between: 120.49997, 120.49998, 120.49999, etc. In fact, the probability of the continuous signal being exactly 120.5 millivolts is infinitesimally small. For example, a pdf of 0.03 at 120.5 does not mean that the a voltage of 120.5 millivolts will occur 3% of the time. The vertical axis of the pdf is in units of probability density, rather than just probability. The probability density function (pdf), also called the probability distribution function, is to continuous signals what the probability mass function is to discrete signals. There is an excellent explanation about this in the chapter 2 of the book The Scientist and Engineer's Guide to Digital Signal Processing.pdf.
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