Point P is at the origin of the coordinate plane. The following trial is performed using one die. When the die is rolled and the number shown is 2 or less, point P is moved 3 units in the positive direction of the $x$-axis, 3 or more, point P is moved 1 unit in the positive direction of the $y$-axis. This trial is repeated 15 times, and the distance between the moved point P and the line $3 x + 4 y = 0$ is the random variable $X$. What is the value of $\mathrm { E } ( X )$? [4 points] (1) 13 (2) 15 (3) 17 (4) 19 (5) 21
Point P is at the origin of the coordinate plane. The following trial is performed using one die.
When the die is rolled and the number shown is\\
2 or less, point P is moved 3 units in the positive direction of the $x$-axis,\\
3 or more, point P is moved 1 unit in the positive direction of the $y$-axis.
This trial is repeated 15 times, and the distance between the moved point P and the line $3 x + 4 y = 0$ is the random variable $X$. What is the value of $\mathrm { E } ( X )$? [4 points]\\
(1) 13\\
(2) 15\\
(3) 17\\
(4) 19\\
(5) 21