The following table shows the probability distribution of a discrete random variable \(X\), for \(1 \leq X \leq 6\), such that
\(P(X = 1) = k\) and \(P(X = r + 1) = \frac{1}{2}P(x = r)\)
where \(r \in \mathbb{Z}^+, 1 \leq r \leq 5\) and \( k \in \mathbb{R}\).
| \(x\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) |
|---|---|---|---|---|---|---|
| \(P(X = x)\) | \(k\) | \(a\) | \(\frac{8}{63}\) | \(\frac{k}{8}\) | \(b\) | \(\frac{1}{63}\) |
Write down an expression in terms of \(k\) for
\(a\);
\(b\).
[2]Find the value of \(k\).
[2]Hence, find the value of \(E(X)\).
[2]Need help? Join our JC Math tuition classes.
Learn more