Abstract
Let us recall that a Normal random variable with parameters (μ, σ2), where μ ∈ R and σ2 > 0, is a random variable whose density is given by:
Such a distribution is usually denoted N(μ, σ2). For convenience of notation, we extend the class of normal distributions to include the parameters μ ∈ R and σ2 = 0 as follows: we will denote by N(μ, 0) the law of the constant r.v. equal to μ (this is also the dirac measure at point μ). Of course, the distribution N(μ, 0) has no density, and in this case we sometimes speak oF a degenerate normal distribution. When μ = 0 and σ2 = 1, we say that N(0, 1) is the standard Normal distribution.
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© 2004 Springer-Verlag Berlin Heidelberg
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Jacod, J., Protter, P. (2004). Gaussian Random Variables (The Normal and the Multivariate Normal Distributions). In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55682-1_16
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DOI: https://doi.org/10.1007/978-3-642-55682-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43871-7
Online ISBN: 978-3-642-55682-1
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