A discrete random variable X has probability density function P(X=x) = k/x for x=2, 4, 6, 8. Find the value of k.

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Question 13:
The probability density distribution function of a discrete random variable $X$ is given by $P(X=x) = \frac{k}{x}$ for $x=2, 4, 6, 8$.

a) Find the value of $k$.

Step 1: The sum of all probabilities for a discrete distribution must equal 1.

$$\sum P(X=x) = 1$$ $$P(X=2) + P(X=4) + P(X=6) + P(X=8) = 1$$ $$$$