Question 16: (3 points) The distribution function of a. random variable X is shown below: Random variable Y has mean 6 and variance 2.05. Correlation between X and Y is [).23. Valuequ X22 X23 X24 Probability [J .3 [1.25 [1.45 Find variance of X 3V: Answer 16: pix = [1.3 x 2 + [1.25 x 3+ [1.45 x 4 = 3.1-5 0; = 0.3 x (2 3.1.5)2 0.25 x (3 3.1.5)2 + 0.45 x (4 3.1.5)2 = 0.7275 01%\". 2 (Jr?{ + 320% 2r(l)(3)JXU}- = 0.7275 + 9 x 2.05 2 x (0.23) x 3 x gum/0.7275 % 20.86