Question
The random variable $X$ can take only the values $0, 1, 2, 3.$ Given that $P(2) = P(3) = p$ and $P(0) = 2P(1)$. If $\Sigma p_ix_i^2 = 2\Sigma p_ix_i,$ find the value of $p.$
| $\text{x}_{\text{i}}$ | $\text{p}_{\text{i}}$ | $\text{p}_{\text{i}}\text{x}_{\text{i}}$ | $\text{p}_{\text{i}}\text{x}^{2}_{\text{i}}$ |
| $0$ $1$ $2$ $3$ |
$\text{2q}$ $\text{q}$ $\text{p}$ $ \text{p}$ |
$0$ $\text{q}$ $\text{2p}$ $\text{3p}$ |
$0$ $\text{q}$ $\text{4p}$ $\text{9p}$ |
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