4. (15 points] a. Explain, in words, Why we must always have that E((X 4)2) 2 0 for any discrete, nite random variable? What if X is discrete but not necessarily nite? b. For any random variable X with events A and B , assume Prob(A) : 1/10 and Prob(B) : 1/4. What are the largest and smallest possible values for Prob(A ['1 B)? What is the largest and smallest possible values for Prob(A U B)? c. For any random variable X with events A and B , let AABZ{mEAUBsuchthatxgAB}. Prove that Prob(AAB) = Prob(A] + Prob(B) 2Prob(A F] B)