Discrete Random Variables (DRV)
Discrete Random Variables (DRV)
IB AA SL: core and optional content
Core: find p and expectation. Optional: variance.
The discrete random variable \(X\) has probability distribution as shown in the table below, where \(p\) is a constant. Show that \(p=\frac{5}{9}\).
| \(x\) | \(0\) | \(1\) | \(2\) | \(3\) |
|---|---|---|---|---|
| \(\mathrm{P}(X=x)\) | \(p\) | \(\frac{1}{2}p\) | \(\frac{1}{4}p\) | \(\frac{1}{20}p\) |
Find \(\mathrm{E}(X)\) and \(\mathrm{Var}(X)\), giving your answers as exact fractions.
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Answer:\(\mathrm{E}(X) = \dfrac{23}{36}\), \(\mathrm{Var}(X) = \dfrac{875}{1296}\)
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