Question 4.128

4.128 Difference between heads and tails.

In Exercise 4.125, the mean and standard deviation were computed directly from the probability distribution of random variable . Instead, define as the number of heads in the three flips, and define as the number of tails in the three flips.

  1. Find the probability distribution for along with the mean and standard deviation .
  2. Find the probability distribution for along with the mean and standard deviation .
  3. Explain why the correlation between and is .
  4. Define as . Use the rules of means and variances along with to find the mean and standard deviation of . Confirm the values are the same as found in Exercise 4.125.