If X is a random variable with possible outcomes 0, 0 and -2, with P( X = 0) = 0.1 and P( X = 0 ) = 0.1, then var(X) is

The variance of a random variable is a measure of how much the values of the variable vary around the expected value. It is calculated as the sum of the squared differences between each possible outcome and the expected value, each multiplied by their respective probabilities.

However, in your question, there seems to be a mistake. You've mentioned the outcome 0 twice with the same probability.

If we assume that the probability of X = 0 is 0.1 for each occurrence, then the total probability for X = 0 would be 0.1 + 0.1 = 0.2.

Given that the only other outcome is -2, the probability of X = -2 must be 0.8 (because the sum of the probabilities of all possible outcomes must equal 1).

Step 1: Calculate the expected value (E(X)).

E(X) = (0 * P(X = 0)) + (-2 * P(X = -2)) = (0 * 0.2) + (-2 * 0.8) = 0 - 1.6 = -1.6

Step 2: Calculate the variance.

Var(X) = ((0 - (-1.6))^2 * P(X = 0)) + ((-2 - (-1.6))^2 * P(X = -2)) = ((1.6)^2 * 0.2) + ((-0.4)^2 * 0.8) = (2.56 * 0.2) + (0.16 * 0.8) = 0.512 + 0.128 = 0.64

Therefore, the variance of X is 0.64.