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Sums and Differences of Independent Random Variables

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Transforming Random Variables

When you add or subtract a constant from the outcomes of a random variable, the mean will increase or decrease by that amount, and the standard deviation will stay the same.

Example:  This distribution is called X.

μXσX=3=1

If we add 2 to the distribution, it becomes X + 2.  Now the distribution has a mean of 5, but the standard deviation is still 1:

μX+2σX+2=5=1

When you multiply or divide the outcomes of a random variable by a constant, the mean and the standard deviation will also be multiplied or divided by that constant.

Example: This distribution is called Y.
μY=3 
σY=1 

Let’s see what happens if we multiply each outcome by 3, and find μ3Y and σ3Y :

 μ3Y=3×3=9 

σ3Y=1×3=3 

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