A Mathematical Model for Finding Bivariate Normal distribution in normal women for Luteinizing Hormone and Progesterone

摘要

A very important property of jointly random normal variables and which will be starting point for our development, is done zero correlation implies independent. This property can be verified by using multivariate transform suppose U and V are independent zero mean normal random variables and that X = aU+bV and Y = cU+dV, so that X and Y are jointly normal. The exponent term q(x,y) is the quadratic form of x and y is obtained. The more general case when x and y are dependent a typical contour is described by an ellipse and it is utilized for our application part. The original definition of LPD is a corpus luteum defective in progesterone secretion, which in turn was a cause of infertility or early spontaneous abortion. Here we have considered Luteinizing hormone (LH) and Progesterone as Bivariate normal and corresponding quadratic function q(x,y) is obtained when they are correlated.