If the random variable X has the following probability distribution: x -1 0 1 2 P(X = x) k 2k 3k $\frac{k}{2}$ then P(X ≤ 0) is equal to:

$\frac{6}{13}$ $\frac{4}{13}$ $\frac{2}{13}$ $\frac{3}{7}$

$\frac{6}{13}$

In the given problem we have  x -1 0 1 2 P(X = x) k 2k 3k   k/2   We know that the sum of total probability will always equal to one so, k +2k + 3k + k/2 = 1 ⇒ k = 1/3 Now P(X ≤ 0) = P(0) + P(-1)                      = 2k + k                      = 3k                 Since k = 1/13 Hence P(X ≤ 0) = 3/13