4. show that for any bounded linear operator t on h, the operators t-t 1 1 т. (t+т*) 2 (t-т*) and = 2i self-adjoint. show that are т%-dti+ itz, т*- t,- it2. show uniqueness, that is, t1+ it2= s1+is2 implies s = t and s2 t2; here, s, and s2 are self-adjoint by assumption.

Match the vocabulary to the proper definition. in probability, two events in which 1. conditional probability the outcome of one event is independent of the outcome of a second event. 2. dependent events in probability, two events in which the outcome of one event is dependent on the outcome of a second event. the probability of an event in which the outcome of the event is conditional on the outcome of one or more different events. 3. independent events