The probability distribution for a random variable Y is given below. Find the mean, variance, and standard deviation of Y. \\[0.5em] \begin{array}{c|cccc} y & 0 & 1 & 2 & 3 \\ \hline p(y) & \frac{1}{8} & \frac{1}{4} & \frac{3}{8} & \frac{1}{4} \end{array}