Problem: Consider a random variable X which takes on values 1 and 2 with probability 0.25 and 0.75, respectively (i.e., P[x = 1] = 0.25 and P[x = 2] = 0.75).
1. Determine the mean and variance of X.
2. Plot the probability density function (pdf) and cumulative distribution function (CDF) of X.
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