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Is the product of two sub Gaussian random variables sub-exponential?
Using Orlicz norms allows to straightforwardly implies the following facts: 1. squared Sub-Gaussian random variable is Sub-Exponential. 2. product of two Sub-Gaussian random variables is Sub-Exponential. Lemma 5.6 (Concentraiton of a sub-gaussian random vector) Let X= (X. 1;:::;X.
Where did the name subgaussian random variables come from?
The name \\subgaussian” is the English counterpart of the French \\sous-gaussienne” coined by Kahane in [3]. Subsequent works have studied subgaussian random variables and processes either per se or in connection with various other subjects.
When did Kahane introduce the subgaussian random variable?
To the best of the author’s knowledge, subgaussian random variables were introduced by Kahane in [3], where they played a role to establish a sucient condition for the almost-sure uniform convergence of certain random series of functions.
Is the tail of a Gaussian random variable zero?
The fact that a Gaussian random variable Z has tails that decay to zero exponentially fast can also be seen in the moment generating function (MGF) M : s → M(s) = IE[exp(sZ)].
What are the properties of an exponential random variable?
Here, we present and prove four key properties of an exponential random variable. The exponential probability density function: for x ≥ 0 and θ > 0 is a valid probability density function. Proof: Is the exponential PDF a valid PDF?
Is the exponential probability density function a valid PDF?
The exponential probability density function: for x ≥ 0 and θ > 0 is a valid probability density function. Proof: Is the exponential PDF a valid PDF?
Which is the easiest case for transformations of continuous random variables?
The easiest case for transformations of continuous random variables is the case of gone-to-one. We \\frst consider the case of gincreasing on the range of the random variable X. In this case, g1is also an increasing function. To compute the cumulative distribution of Y = g(X) in terms of the cumulative distribution of X, note that F