A randomiser machine produces normally distributed random real numbers with fixed but unknown mean and variance. These numbers are fed to a computer that outputs zero for numbers strictly between 1 and 1, 1 if the number is greater or equal to 1, and -1 if the number is less or equal to -1. In other words, the original normally distributed variable with mean and standard deviation , X~ converted into another random variable Y = g(X), where Find the following probabilities. g(x) = P(Y= = (a) Researchers have studied the output of the computer and determined that the cumulative distribution function of the output variable Y has the following representation. Fy (y) = P(Y = -1): -1/2): P(-1