* Consider the following joint distribution for the weather in two consecutive days. Let X and Y be the random variables for the weather in the first and the second days, with the weather coded as 0 for sunny, 1 for cloudy, and 2 for rainy. X Y 0 1 2 0 0.3 0.1 0.1 1 0.2 0.1 0 2 0.1 0.1 0 (a) Find the marginal probability mass functions for X and Y . (b) Calculate the expectation and variance for X and Y . (c) Calculate the covariance and correlation between X and Y . Are they correlated