If a discrete random variable x has the following probability distribution :
| X: | 1 | 2 | 3 | 4 |
| P(X): | $\lambda $ | $\lambda^2$ | $2\lambda^2$ | $\lambda $ |
then, the value of $\lambda $ is :
Answer & explanation
Correct answer: option 1
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]