(Probability and Statistics) A coin is tossed three times, and based on the results, a score is obtained as a random variable $X$ according to the following rules. (가) If the same face does not appear consecutively, the score is 0 points. (나) If the same face appears consecutively exactly twice, the score is 1 point. (다) If the same face appears consecutively three times, the score is 3 points. What is the variance $\mathrm{V}(X)$ of the random variable $X$? [3 points] (1) $\frac{9}{8}$ (2) $\frac{19}{16}$ (3) $\frac{5}{4}$ (4) $\frac{21}{16}$ (5) $\frac{11}{8}$
(Probability and Statistics) A coin is tossed three times, and based on the results, a score is obtained as a random variable $X$ according to the following rules.\\
(가) If the same face does not appear consecutively, the score is 0 points.\\
(나) If the same face appears consecutively exactly twice, the score is 1 point.\\
(다) If the same face appears consecutively three times, the score is 3 points.
What is the variance $\mathrm{V}(X)$ of the random variable $X$? [3 points]\\
(1) $\frac{9}{8}$\\
(2) $\frac{19}{16}$\\
(3) $\frac{5}{4}$\\
(4) $\frac{21}{16}$\\
(5) $\frac{11}{8}$