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) = __________.
Answer & explanation
Correct answer: option 4
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 $\frac{1}{2}$.