| $X$ | 0 | 1 | 2 | 3 | Total |
| $\mathrm { P } ( X )$ | $\frac { 2 } { 10 }$ | $\frac { 3 } { 10 }$ | $\frac { 3 } { 10 }$ | $\frac { 2 } { 10 }$ | 1 |
The probability distribution table of random variable $X$ is shown below. Find the variance of random variable $Y = 10 X + 5$. [3 points]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$X$ & 0 & 1 & 2 & 3 & Total \\
\hline
$\mathrm { P } ( X )$ & $\frac { 2 } { 10 }$ & $\frac { 3 } { 10 }$ & $\frac { 3 } { 10 }$ & $\frac { 2 } { 10 }$ & 1 \\
\hline
\end{tabular}
\end{center}