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

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 $Z _ { i } = 2 G _ { i } + 4 Y _ { i } - 1$