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Cogito

AP Statistics · Chapter 2 · Lesson 2

Practice Worksheet

Random Variables

Mean and standard deviation of a distribution.

12 problems · about 22 minutes · VAR-5.A, VAR-5.D

NameDate

Figure — use these to answer the problems

The distribution of two-dice totals. The middle values have more ways to occur, so they carry more probability.
Total 43
Total 54
Total 65
Total 76
Ways to make 43
Ways to make 54
Ways to make 65
Ways to make 76
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Independent, standard deviations 5 and 12. Standard deviation of the sum?

    Answer

  2. What happens to variances when independent variables are subtracted?

    • They add, exactly as for a sum.
    • They subtract.

  3. Values 0, 1, 2 with probabilities 0.25, 0.5, 0.25. Mean?

    Answer

  4. Standard deviations 6 and 8, independent. Standard deviation of the sum?

    Answer

  5. X has mean 20. What is the mean of X + 5?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. X has standard deviation 4. What is the standard deviation of X + 5?

    Answer

  2. X has standard deviation 4. What is the standard deviation of 3X?

    Answer

  3. Independent with variances 9 and 16. Variance of the difference?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each quantity by whether adding a constant changes it.

    Write each item under the heading it belongs to: The mean · The median · The standard deviation · The variance

    Changes

    Unchanged

  2. Values 2 and 6 with probabilities 0.5 each. Mean?

    Answer

  3. The Sum

    X has mean 10 and Y has mean 4. What is the mean of X + Y?

    Answer

  4. The Spread

    Independent, with standard deviations 3 and 4. What is the standard deviation of the sum?

    Answer