Help me solve this exercise.

DIS. 7. Cantelli's inequality. Let X be a random variable with finite variance, o2. (a) Prove that, for 1>0, 02 P(X - EX > 3) ) 22 +02 (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) E XCOV3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound ov2. (e) Generalize Cantelli's inequality to moments of order r 71. DIS. 7. Cantelli's inequality. Let X be a random variable with finite variance, o2. (a) Prove that, for 1>0, 02 P(X - EX > 3) ) 22 +02 (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) E XCOV3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound ov2. (e) Generalize Cantelli's inequality to moments of order r 71