breaks down. The approximation (**) for the integral holds for functions that are 'smooth' in a certain sense, but there are probability distributions for which it does not hold. In fact there are distributions G for which \int_{-a}^{a} dz G(x - z) = Chi_{a}(x) , Thanks. If \int_{-a}^{a} dz G(x - z) = Chi_{a}(x), then x must not be a continuous random variable, but a
Suppose X and Y are two continuous, independently and identically distributed random variables. For example, both of them are in standard normal distribution N(0,1). What is the probability of equality between X and Y, Pr(X=Y)? Is it infinitesimal? but in the following way I find Pr(X=Y)=1/(2*sqrt(Pi)): Let INT denote an integral from minus infinity to plus infinity, then Pr(X=Y)=INT( Pr(X
Hi John, John O'Flaherty <quiasmox@yeeha.com> writes: On Fri, 18 Apr 2008 22:13:38 -0400, Randy Yates <yates@ieee.org> wrote: I recently examined the feasibility of generating noise for testing a communication system and came to the disappointing conclusion that generating a digital signal and then converting it to analog via an ADC will never be capable of generating a stationary
On Fri, 18 Apr 2008 22:13:38 -0400, Randy Yates <yates@ieee.org> wrote: I recently examined the feasibility of generating noise for testing a communication system and came to the disappointing conclusion that generating a digital signal and then converting it to analog via an ADC will never be capable of generating a stationary, continuous random process (signal) with an arbitrary distribution
