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 0.2 0.2 0.2
1 0.1 0.1 0.1
2 0 0.1 0

Required:
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?
d. Are the weather in two consecutive days independent?