The probability distribution of a random variable X is given as under :

$P(X=x)=\left\{\begin{array}{cc}
K x^2 & \text { for } x=1,2,3 \\
2 K x & \text { for } x=4,5,6 \\
0 & \text { otherwise, }
\end{array}\right.$

where K is a constant. Then P(x < 4) is equal to:

$\frac{7}{22}$

The correct answer is Option (2) → $\frac{7}{22}$

$\sum P(X=x)=1$

$K(1^2+2^2+3^2) + 2K(4+5+6)=1$

$K(1+4+9) + 2K(15)=1$

$14K + 30K = 44K = 1 \Rightarrow K=\frac{1}{44}$

$P(X<4)=P(1)+P(2)+P(3)=K(1^2+2^2+3^2)$

$=14K=\frac{14}{44}=\frac{7}{22}$

$P(X<4)=\frac{7}{22}$