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 q, X ~ N(/, 62), is converted into another random variable Y = g(X), where -1, if a 1. (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. 0, if y 1. Find the following probabilities. P(Y = 1): P(Y =! ):Find the following probabilities. P(Y = 1): P(Y - P( 1