The variance of X would be 2/9. This is because, since each letter is placed randomly into one of the three addressed envelopes, the probability of any letter going into a specific envelope is 1/3. As the three letters are independent of each other and the probability of any letter going into a specific envelope is 1/3, the variance of X is the sum of the variances of the individual Bernoulli random variables. Each Bernoulli random variable has variance p(1-p) = (1/3)(1-1/3) = 1/3 * 2/3 = 2/9 . Therefore, the variance of X is 2/9