please answer all parts

X and Y are joint random variables that have a uniform distribution over the shaded area pictured below. Y 1- 1 X (a) (5 points.) Compute the marginal PDF fx(x). Explain your reasoning for full credit with words, sketches, and/or computations. Remember to specify the PDF at all values of x. (b) (5 points.) Determine E(Y). (c) (5 points.) Are X and Y independent? Justify your answer clearly. (d) (5 points.) Suppose we knew that the correlation of X and Y was equal to 1. Determine whether the correlation coefficient p is exactly 0 exactly 1 exactly -1 positive in the range (0,1) negative in the range (-1,0) and explain your answer.