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For k > 1, the density function tends to zero as x approaches zero from above, increases until its mode and decreases after it. The density function has infinite negative slope at x = 0 if 0 < k < 1, infinite positive slope at x = 0 if 1 < k < 2 and null slope at x = 0 if k > 2. For k = 1 the density has a finite negative slope at x = 0.
Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass. Other conceptually comparable quantities or ratios include specific density, relative density (specific gravity), and specific weight.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.
The density () has its peak at = and inflection points at = + and =. Although the density above is most commonly known as the standard normal, a few authors have used that term to describe other versions of the normal distribution.
Assuming (,) is a.e. twice differentiable, we start by using the relationship between joint probability density function (PDF) and joint cumulative distribution function (CDF) and its partial derivatives.
Ad-Free AOL Mail is only available when viewing email on the web from a computer or mobile device. If you access AOL Mail from the AOL Desktop software or mobile app, you will continue to see paid ...
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