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1 penny / 1 die (Posted on 2011-05-06) Difficulty: 3 of 5
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?

See The Solution Submitted by Jer    
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re: some solutions, but not sure about standard deviations | Comment 2 of 5 |
(In reply to some solutions, but not sure about standard deviations by Charlie)

Your standard deviations are both _way_ too small.  Using Chebyshevs Theorem it is not true that at least 3/4 of the probability is within two standard deviations of the mean. 

In line 440 is (I-sum) really (x-mean)?
  Posted by Jer on 2011-05-06 15:52:41

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