Mydriasis eye, and also to reduce painful ciliary muscle spasm (see cycloplegia). One effect of administration of a mydriatic is intolerance to bright light (photophobia). Purposefully-induced mydriasis via mydriatics is also used as a diagnostic test for Horner's syndrome. Mydriasis can be induced via modulation of adrenergic or cholinergic signalling. Within the adrenergic system, norepinephrine is a hormone and neurotransmitter responsible for regulating physiological processes in the body, including the involuntary muscles of the autonomic nervous system (such as the dilation or constriction of the pupil aperture via the muscles of the iris). Modulation of norepinephrine signalling can induce mydriasis. For
Sum of normally distributed random variables more general case we find that the closest point on the line to the origin is located a (signed) distance away, so that The same argument in higher dimensions shows that if then Now we are essentially done, because So in general, if then In the event that the variables "X" and "Y" are jointly normally distributed random variables, then "X" + "Y" is still normally distributed (see Multivariate normal distribution) and the mean is the sum of the means. However, the variances are not additive due to the correlation. Indeed, where ρ is the correlation. In particular, whenever ρ