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Calculating the Variance from a linear function W = X + Y
I have been given a joint probability distribution of the following X1 and X2, and Y0 and Y1. The distribution is equally 0.25. We are asked to calculate the Marginal Probability (0.50 in each value), the Covariance and Correlation for X and Y, which I have calculated as 0 in both cases, and then we are asked to compute the mean and variance for the linear function W = X + Y. I calculated the mean to be (1 + 2)/2 + (0 + 1)/2 = 2 which is correct according to the answer sheet. However I have used the following formula to find the variance: Variance = 1/N{The sum of} [xi - (the mean of x)]^2. I calculate the solution to be 1/4(0 - 2)^2+(1 - 2)^2+(1 - 2)^2+(2 - 2)^2 = 1.5, but the answer script says 0.5. I just wanted to know where I was making a mistake. Thanks so much. Adrian.
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