JEE Main 2025 — 7 April, Evening Shift — Question 27

$P(X=0)=P(X=1)=p$ and $P(X=2)=P(X=3)=q$

$2 p+2 q=1$

$$\begin{gathered} \Rightarrow p+q=\frac{1}{2} …(i) \end{gathered}$$

$E\left(X^{2}\right)=2 E(x)$

$P\left(0^{2}\right)+p(1)^{2}+q(2)^{2}+q(3)^{2}$

$=2(p(0)+p(1)+q(2)+q(3))$

$$\begin{gathered} \Rightarrow \quad p=3 q ..(ii) \end{gathered}$$

For (1) and (2)

$q=\frac{1}{8}$ and $p=\frac{3}{8}$

$8 p-1=2$