Search results
Results from the WOW.Com Content Network
A much simpler result, stated in a section above, is that the variance of the product of zero-mean independent samples is equal to the product of their variances. Since the variance of each Normal sample is one, the variance of the product is also one. The product of two Gaussian samples is often confused with the product of two Gaussian PDFs.
The product of two Gaussian probability density functions (PDFs), though, is not in general a Gaussian PDF. Taking the Fourier transform (unitary, angular-frequency convention) of a Gaussian function with parameters a = 1 , b = 0 and c yields another Gaussian function, with parameters c {\displaystyle c} , b = 0 and 1 / c {\displaystyle 1/c ...
For example, four iterations of a moving average yield a cubic B-spline as a filter window, which approximates the Gaussian quite well. A moving average is quite cheap to compute, so levels can be cascaded quite easily. In the discrete case, the filter's standard deviations (in the time and frequency domains) are related by
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra. [28 ...
This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]
The other prime numbers are not Gaussian primes, but each is the product of two conjugate Gaussian primes. A Gaussian integer a + bi is a Gaussian prime if and only if either: one of a, b is zero and the absolute value of the other is a prime number of the form 4n + 3 (with n a nonnegative integer), or
The use of Gaussian orbitals in electronic structure theory (instead of the more physical Slater-type orbitals) was first proposed by Boys [2] in 1950. The principal reason for the use of Gaussian basis functions in molecular quantum chemical calculations is the 'Gaussian Product Theorem', which guarantees that the product of two GTOs centered on two different atoms is a finite sum of ...