Let [math]X[/math] be a random variable with cumulative distribution function [math]F_X[/math], and let [math]Y = X + b[/math], [math]Z = aX[/math], and [math]W = aX + b[/math], where [math]a[/math] and [math]b[/math] are any constants. Find the cumulative distribution functions [math]F_Y[/math], [math]F_Z[/math], and [math]F_W[/math]. Hint: The cases [math]a \gt 0[/math], [math]a = 0[/math], and [math]a \lt 0[/math] require different arguments.