The random variable X has a probability distribution P(X) of the following from where k is a scalar and

$P(X=x)= \left\{\begin{matrix}k, & if & x=0\\2k, & if & x=1\\3k, & if & x=2\\0, & & otherwise \end{matrix}\right.$

then value of P(X< 2) = __________.

$\frac{1}{2}$

Given

$P(X=0)=k,\;P(X=1)=2k,\;P(X=2)=3k$

Total probability $=1$

$k+2k+3k=6k=1$

$k=\frac{1}{6}$

Now

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

$=k+2k=3k$

$=3\cdot\frac{1}{6}$

$=\frac{1}{2}$

The value of $P(X<2)$ is $\frac{1}{2}$.