A fair six sided die can roll any number from 1 to 6 with equal likelihood.
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?

(In reply to re(2): some solutions, but not sure about standard deviations by Charlie)

Corrected standard deviation is 2.7271780286589286028 in both experiments: A and B.

Faulty lines were

Sumsq=(I-Sum)*(I-Sum)*Prob(I)

which should have been, of course:

Sumsq=Sumsq+(I-Sum)*(I-Sum)*Prob(I)

BTW, that's sqrt(119/16) = sqrt(119)/4.

Posted by Charlie on 2011-05-07 03:28:06