A random variable has the following probability distribution $X=x_i$ 2 3 4 5 $P(X=x_i)$ 4k k 5k 2k The value of P(X < 3) is :

$\frac{1}{12}$ $\frac{1}{3}$ $\frac{1}{4}$ $\frac{5}{12}$

$\frac{1}{3}$

The correct answer is Option (2) → $\frac{1}{3}$ From the given table we know that $∑pi=1$ so $4k+k+6k+2k=1$ $12k=1⇒k=\frac{1}{12}$ so $P(X < 3)=4k=\frac{1}{3}$