Question: Difference between heads and tails. In Exercise 4.125, the mean and standard deviation were computed directly from the probability distribution of random variable D. Instead,

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

(a) Find the probability distribution for X along with the mean mX and standard deviation sX .

(b) Find the probability distribution for Y along with the mean mY and standard deviation sY .

(c) Explain why the correlation r between X and Y is 21.

(d) Define D as X 2 Y. Use the rules of means and variances along with r 5 1 to find the mean and standard deviation of D. Confirm the values are the same as found in Exercise 4.125.

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