The probability distribution for the random variable Y is given as:

Here's how to solve the problem:

The probability distribution for the random variable $Y$ is given as:

$Y$	0	1	2	3	4
$p(y)$	$\frac{1}{8}$	$2k$	$\frac{1}{6}$	$3k$	$\frac{2}{7}$

Step 1: Find the value of $k$.
The sum of all probabilities in a probability distribution must equal 1.

$$\sum p(y) = 1$$ $$$$