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?

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9