2024 VJC P2 Q6
2024 VJC P2 Q6
Prelims
A random variable \(X\) has the probability distribution given in the following table.
\(x\) | \(1\) | \(4\) | \(6\) | \(8\) |
|---|---|---|---|---|
\( \mathrm{P} (X = x) \) | \(a\) | \(b\) | \(c\) | \(d\) |
Given that \(E(X)=4\), \(\mathrm{Var}(X)=\frac{19}{4}\), and \( \mathrm{P}(X<4)=\mathrm{P}(X>4)\), find the values of \(a\), \(b\), \(c\) and \(d\).
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Answer:\(a=\frac{1}{4}\), \(b=\frac{1}{2}\), \(c=\frac{1}{8}\) and \(d=\frac{1}{8}\).
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