Suppose that z is a continuous random variable with mean 0 and variance 1. In addition, suppose that the density function of z is symmetric with respect to the y-axis. Let ? = a+bz, where a and b are two non-zero constants. Prove that P(0 ? ? ? a ? |ab|) ? 1 2 ? 1 2a 2 .

Suppose that z is a continuous random variable with mean 0 and variance 1. In addition, suppose that the density function of z is symmetric with respect to the yaxis. Let n = a+bz, where a and b are two nonzero constants. Prove that L l P . (0-12 a_labl)_2 2G2