1. **State the problem:** We are given a probability distribution table for a discrete random variable $X$ with values $0,1,2,3,4,5,>5$ and corresponding probabilities $0.54,0.26,0.15,k,0.01,0.01,0.00$. We need to find the value of $k$. 2. **Recall the rule for probabilities:** The sum of all probabilities for a discrete random variable must equal 1. That is, $$\sum P(X=x) = 1$$ 3. **Set up the equation:** Using the given probabilities, $$0.54 + 0.26 + 0.15 + k + 0.01 + 0.01 + 0.00 = 1$$ 4. **Simplify the known values:** $$0.54 + 0.26 = 0.80$$ $$0.80 + 0.15 = 0.95$$ $$0.95 + 0.01 + 0.01 = 0.97$$ 5. **Write the equation with simplified sum:** $$0.97 + k = 1$$ 6. **Solve for $k$:** $$k = 1 - 0.97 = 0.03$$ 7. **Interpretation:** The missing probability $k$ is $0.03$ to ensure the total probability sums to 1. **Final answer:** $$\boxed{0.03}$$