I understand if a fair coin is tossed repeatedly, the probability of getting a head during each toss does not change and is independent from that of other tosses.
What about the number of tosses required to get heads - are they dependent?
For example let X be the random variable representing number of tosses required to get the first head, and Y the random variable representing the number of tosses to get the first two heads. Are the two variables dependent?
Intuitively it seems that Y depends on X. What is a more 'formal' reasoning than mere intuition?