CK-12 Probability and Statistics - Advanced

7.5. Sums and Differences of Independent Random Variables http://www.ck12.org

μx=∑xipi μy=∑xipi

μX= 3. 5 μY=− 3. 5

σ^2 x≈∑(xi−μx)^2 pi σ^2 y≈∑(xi−μy)^2 pi

σ^2 x≈ 2. 917 σ^2 y≈ 2. 917

μX+Y=μX+μY μX+Y=μX−μY

μX+Y= 3. 5 +(− 3. 5 ) = 0 μX−Y= 3. 5 −(− 3. 5 ) = 7

σ^2 X+Y=σ^2 X+σ^2 Y σ^2 X−Y=σ^2 X+σ^2 Y

σ^2 X+Y≈ 2. 917 + 2. 917 = 5. 834 σ^2 X−Y≈ 2. 917 + 2. 917 = 5. 834

Notice how the expected values and the variances combine for these two experiments.

Example:

I earn $25.00 an hour for tutoring but spend $20.00 an hour for piano lessons. I save the difference between my
earnings for tutoring and the cost of the piano lessons. The number of hours I spend on each activity in one week
varies independently according to the probability distributions shown below. Determine my expected weekly savings
and the standard deviation of these savings.

TABLE7.20:

Hours of Piano Lessons,x Probability,p

0 0. 3

1 0. 3

2 0. 4