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Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability5 Marks
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 $p.$
✓

Answer

$\text{x}_{\text{i}}$ $\text{p}_{\text{i}}$ $\text{p}_{\text{i}}\text{x}_{\text{i}}$ $\Sigma p_ix_i{}^2$
$0$
$1$
$2$
$3$		 $\text{2q}$
$\text{q}$
$\text{p}$
$ \text{p}$		 $0$
$\text{q}$
$\text{2p}$
$\text{3p}$		 $0$
$\text{q}$
$\text{4p}$
$\text{9p}$
$\Sigma pi = 1 \Rightarrow 3q + 2p= 1..(1)$
from $(1)$ and $(2), p = \frac{1}{11}$

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