Please give a detailed step-by-step answer for this one problem. For prep in 210. I am struggling, thank you.

Problem 4 Consider two events A and B such that P(A) : %, P(B l A) = %, and P(A l B) = i. Let the random variables X and Y be dened as X = 1 or 0 depending on whether the event A has occurred or has not occurred, and Y = 1 or 0 depending on whether the event B has or has not occurred. Answer the following questions. (i) Are the random variables X and Y independent? (ii) Determine the probability P(X2 + Y2 = 1). (iii) Determine the probability P(XY = X2 Y2). (iv) Is the random variable X uniformly distributed on the interval 0 to 1? (v) Are the random variables X and Y identically distributed