Answer to Problem 1: .9628
Answer to Problem 2: a) C=3/2 b) (3/2)(x-x^3/3)
Answer to Problem 3: (1/4sqrt(2*Pi)) * exp(-(x-2)^2/32)
Answer to Problem 4: 7/6
Answer to Problem 5: For x between [0,1], 4*integral(1-x+t)(1-t) from 0 to x; For x between [1,2], 4* integral(1-x+t)(1-t) from 1 to x; For all other x, the answer is zero.
Answer to Problem 6: a) 1/2 inside the rectangle with coordinates (1,0), (0,1), (-1,0) and (0,-1) and zero outside. b) f_X (x) = 1+x for x between [-1,0] and 1-x for x between [0,1], zero otherwise. c) No
Answer to Problem 7: .4218