Consider the set of points in the set C: C={(x, y)|x, y∈ℤ,x2+|y|≤2}. Suppose that we pick a point (X, Y) from this set completely at random. Thus, each point has a probability of 111 of being chosen. Find the joint and marginal PMFs of X and Y. Find the conditional PMF of X given Y=1. Are X and Y independent? Find E[XY2].

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?