You Do It

  1. 33.

    1. E(2X − 100) = 1900; SD(2X − 100) = 400

    2. E(0.5Y) = 1000; SD(0.5Y) = 300

    3. E(X + Y) = 3000; SD(X + Y) ≈ 632.5

    4. E(X − Y) = − 1000; SD(X + Y) ≈ 632.5

  2. 35. All of the calculated expected values remain the same. Only the variances and standard deviations change. Unless both X and Y appear, the variance is the same.

    1. Unchanged

    2. Unchanged

    3. SD(X + Y) ≈ 651.9

    4. SD(X − Y) ≈ 612.4

  3. 37. − 0.2

  4. 39.

    1. These are dependent, because for example we can write Y = 60 − X.

    2. Since X + Y = 60, the variance is 0.

  5. 41.

    1. Let X1 and X2 denote the deliveries for the two. Both drivers are said to operate independently. We assume that the number of deliveries is comparable as well.

    2. E(X1 + X2) = 12 deliveries SD(X1 + X2) ≈ 2.83 deliveries

    3. E(X1 + 1.5X2) = 15 hours

    4. SD(

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