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3. Let X m Geometric[p) with p E (III, 1). Prove that for every o, b E N we have PIX =o+b|X I? o}=P{X 2b). 4. Let X be a discrete random variable with the following distribution: P(X=3]I=o, P[X=2}=%, P[X=1)=b, P(X=l]}=%, P(X=1)=e, P(X=2}=% 3,. Find it, I}, e. h. Calculate E{3 + 21'}, E|{3 + 2X)\