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2 answers:
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With 10 integers available, 
has PMF
We're interested in the statistics of the new random variable
. To do this, we need to know the PMF for 
. This isn't too hard to find.
Since the PMF for gives a value of 
whenever 
is an integer between 0 and 9, it follows that 
must also be an integer for the PMF to give the identical value of . This means
Now the mean (expectation) is
The variance would be
The standard deviation is the square root of the variance, so you have
We're interested in the statistics of the new random variable
Since the PMF for
Now the mean (expectation) is
The variance would be
The standard deviation is the square root of the variance, so you have