Howtosignalprocessing
- Is the product of Gaussians Gaussian?
- What is the product of two Gaussian distributions?
- What is the PDF of a Gaussian?
- Is the product of two PDFs a PDF?
Is the product of Gaussians Gaussian?
Since the product of two Gaussians is a Gaussian, the posterior probability is Gaussian.
What is the product of two Gaussian distributions?
The product of two Gaussian PDFs is proportional to a Gaussian PDF with a mean that is half the coefficient of x in Eq. 5 and a standard deviation that is the square root of half of the denominator i.e. as, due to the presence of the scaling factor, it will not have the correct normalisation.
What is the PDF of a Gaussian?
The PDF of the Gaussian random variable has two parameters, m and σ, which have the interpretation of the mean and standard deviation respectively. 1 The parameter σ2 is referred to as the variance. An example of a Gaussian PDF is shown in Figure 3.5.
Is the product of two PDFs a PDF?
The product of two normal PDFs is proportional to a normal PDF. This is well known in Bayesian statistics because a normal likelihood times a normal prior gives a normal posterior. But because Bayesian applications don't usually need to know the proportionality constant, it's a little hard to find.
