State the definition of the concept of correlation between two complex random variables X and Y

QUESTION 3 (6 POINTS) (a) State the definition of the concept of correlation between two compler random variables X and Y: cor (X, Y) ./1 (b) State mathematically the definition of the concept of the conditional probability P(A | B), where A and B are two arbitrary events with P(B) > 0: P(A | B) - /1 (c) If a fair coin is tossed independently 10 times and six heads are observed in the outcome, what is the probability that an eleventh toss would produce a heads? P(11th toss is heads) = /1 (d) Prove that if X is a random variable with a finite mean value, then {{X' } 2 84{X]. Hint: Consider var(X?), var(X) and the fact that variance is always a real nonnegative amount