If a discrete random variable x has the following probability distribution :

then, the value of $\lambda $ is :

$\frac{1}{3}$

The correct answer is Option (1) → $\frac{1}{3}$

Since the sum of all probabilities must be 1.

$⇒λ+λ^2+2λ^2+λ=1$

$⇒λ^2+2λ-1=0$

$⇒3λ^2+3λ-λ-1=0$

$⇒3λ(λ+1)-(λ+1)=0$

$⇒(λ+1)(3λ-1)=0$

$⇒λ=\frac{1}{3}$ [Probability is always positive]