Consider a random variable X which takes on values 1, 2, and 3 with probability 0.25, 0.5, and 0.25, respectively (i.e., P[x=1] = 0.25, P[x = 2] = 0.50, and P[x = 3] = 0.25). Determine the mean and variance of X. Plot the probability density function (pdf) and cumulative distribution function (CDF) of X.