A random variable X has the following probability distribution: X = x i - 2 - 1 0 1 2 P X = x i 1 6 k 1 4 k 1 6 The variance of this random variable is

Step-by-step solution

A random variable X has the following probability distribution: X = x i - 2 - 1 0 1 2 P X = x i 1 6 k 1 4 k 1 6 The given distribution is the probability distribution. ∴ 1 6 + k + 1 4 + k + 1 6 = 1 ⇒ k = 5 24 Now, x i P x = x i x i P x i x i 2 P x i - 2 1 6 - 1 3 2 3 - 1 k - k k 0 1 4 0 0 1 k k k 2 1 6 1 3 2 3 ∑ x i P x i = 0 ∑ x i 2 P x i = 4 3 + 2 k Variance = ∑ x i 2 P x i - ∑ x i P x i 2 . = 4 3 + 2 k - 0 = 4 3 + 2 × 5 24 = 7 4