On fair coin, consider heads to have value 2 and tails to have value 1.
Consider the two experiments:
Experiment A: First roll the die. The outcome tells you how many times to flip the coin. x=the total value of the coin tosses.
Experiment B: First flip the coin. The outcome tells you how many times to roll the die. y=the total value of the die rolls.
1. Prove that the probability distributions of x and y are not the same.
2. How do the means of x and y compare?
3. How do the standard deviations of x and y compare?