A random variable X has a probability distribution P(X) of the following form, wher K is some unknown constant :

$P(X-x_i)=\left\{\begin{matrix}2K& , if\, x_i= 0\\Kx_i & , if \, x_i =1\\K(x_i-1) & ,if\, x_i = 2 \, or \, 3\\0& , otherwise\end{matrix}\right.$

The value of K is :

$\frac{1}{6}$

The correct answer is Option (2) → $\frac{1}{6}$

$P(X=0)+P(X=1)+P(X=2)+P(X=3)=1$

$P(X=0)=2k$

$P(X=1)=k$

$P(X=2)=k(x_2-1)=k(2-1)=k$

$P(X=3)=k(x_3-1)=k(3-1)=2k$

$⇒6k=1$

$⇒k=\frac{1}{6}$