The table below shows the probability distribution for a discrete random variable $X$ - AQA - A-Level Maths Mechanics - Question 11 - 2018 - Paper 3

To find the value of $k$, we know that the total probability for a discrete random variable must equal 1. Therefore, we will sum all the probabilities:

$$P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) = k + 2k + 4k + 2k + k = 10k$$

We set up the equation:

$$10k = 1$$

Solving for $k$, we divide both sides by 10:

k = rac{1}{10}

Thus, the value of $k$ is rac{1}{10}. When providing the answer, ensure to circle it to meet the question requirements.