Question

The probability distribution of a random variable is given below: \[\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X = x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(X = x) & 0 & K & 2K & 2K & 3K & K^2 & 2K^2 & 7K^2 + K \\ \hline \end{array}\]

Find \( P(0<X<5) \).

• A. \( \frac{1}{10} \)
• B. \( \frac{3}{10} \)
• C. \( \frac{8}{10} \)
• D. \( \frac{7}{10} \)

Hint:

To solve probability distribution problems, always ensure the total probability sums to 1, then solve for unknown constants accordingly.