A random variable X has the Probability Distribution :
| X | 1 | 2 | 3 | 4 |
| P(X) | $2k^2$ | $k$ | $k$ | $k^2$ |
The value of k is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{1}{3}$
The sum of all probabilities must be 1.
$⇒2k^2+k+k+k^2=1$
$⇒3k^2+2k-1=0$
$⇒(k+1)(k-\frac{1}{3})-1=0$
$⇒k=\frac{1}{3}$ (Probability is always positive)