The Standardized Gaussian PRNG Produces Gi and the PRNG Value $Y _ { i }$

question 1

Essay

The standardized Gaussian PRNG produces Gi and the PRNG value $Y _ { i }$ is uniformly distributed over [0,1).If $\mathrm { G } _ { i } \text { and } Y _ { i }$ are independent, what is the mean and variance of $Z _ { i } = 2 G _ { i } + 4 Y _ { i } - 1$

---

Definitions:

Urinary Bladder

A hollow organ in the lower abdomen that stores urine from the kidneys before it is expelled from the body.

Digestive Tract

A series of hollow organs joined in a long, twisting tube from the mouth to the anus, where digestion of food takes place.

Parasympathetic

Part of the autonomic nervous system responsible for relaxation and conserving energy by slowing down the heart rate and increasing intestinal and gland activity.

Innervation

The supply of nerves to a specific body part, enabling sensation and movement in that area.