The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: Borel's paradox shows that conditional probability density functions need not be invariant under coordinate transformations.
If for discrete random variables P(Y = y | X = x) = P(Y = y) for all x and y, or for continuous random variables pY|X(y | x) = pY(y) for all x and y, then Y is said to be independent of X (and this implies that X is also independent of Y).
Seen as a function of y for given x, P(Y = y | X = x) is a probability and so the sum over all y (or integral if it is a density) is 1. Seen as a function of x for given y, it is a likelihood function, so that the sum over all x need not be 1.
US Patent Issued to Telefonaktiebolaget L M Erricsson (PUBL) on Aug. 23 for "Methods and Arrangements for Noise Rise Estimation" (Swedish Inventor)
Aug 30, 2011; ALEXANDRIA, Va., Aug. 30 -- United States Patent no. 8,005,433, issued on Aug. 23, was assigned to Telefonaktiebolaget L M...
Sampling Errors in the Measurement of Rainfall Parameters Using the Precipitation Occurrence Sensor System (POSS)
Feb 01, 2007; ABSTRACT The Precipitation Occurrence Sensor System (POSS) is a small Doppler radar originally designed by the Meteorological...