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 standard deviations -- of course -- "obvious" problem by Charlie)

I thought this was a neat discovery I made:  two related but quite different looking distributions nevertheless having the same mean and standard deviation.

I'm glad I was able to share this result in perplexus problem form.

Posted by Jer on 2011-05-08 00:18:22