It can be shown that a unique mixed strategy Nash equilibrium exists with the following pair of probability density functions:
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This probability density function gives the probability, per unit speed, of finding the particle with a speed near v.
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In classical mechanics, an ensemble is represented by a probability density function defined over the system's phase space.
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Note that if the probability density function is a function of various parameters, so too will be its normalizing constant.
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Although the probability density function for a general stable distribution cannot be written analytically, the general characteristic function can be.
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Where & phi; ( " x " ) is the probability density function of the standard normal distribution.
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The Gaussian function, which is the probability density function of the normal distribution with mean and standard deviation, naturally contains:
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From this we find the probability density function to have the constant value 1 on the interval ( 0, 1 ).
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Signal mixtures tend to have Gaussian probability density functions, and source signals tend to have non-Gaussian probability density functions.
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Signal mixtures tend to have Gaussian probability density functions, and source signals tend to have non-Gaussian probability density functions.
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