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 $\Sigma$pixi2 = 2$\Sigma$pixi, 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}$ | $0$ $\text{q}$ $\text{2p}$ $\text{3p}$ | $0$ $\text{q}$ $\text{4p}$ $\text{9p}$ |
$\Sigma$pi = 1 ⇒ 3q + 2p= 1..(1)
$\Sigma$pixi2 = 2$\Sigma$pixi ⇒ q = 3p..(2)
from (1) and (2), p = $\frac{1}{11}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.