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Cogito

Probability and Statistics · Chapter 5 · Lesson 2

Practice Worksheet

Random Variables

A number attached to a random outcome.

12 problems · about 21 minutes · TEKS P.S.2.G, S-MD.A.1

NameDate

Figure — use these to answer the problems

The distribution of two-dice totals. The middle values have more ways to occur, so they are taller.
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. Probabilities 0.3, 0.3 and one more. What must it be?

    Answer

  2. What is a random variable?

    • A number attached to each outcome of a random process.
    • A value chosen at random by the statistician.

  3. Probabilities 0.1, 0.4 and one more. What must it be?

    Answer

  4. Values 1 and 3 with probabilities 0.5 each. Mean?

    Answer

  5. Two dice. How many ways to total 7?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Two dice. How many ways to total 2?

    Answer

  2. Number of siblings. Discrete or continuous? 1 discrete, 2 continuous.

    Answer

  3. Exact height. Discrete or continuous? 1 or 2.

    Answer

Stretch Yourself

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

4 problems

  1. Which must be true of a probability distribution?

    • The probabilities total 1
    • Each probability is between 0 and 1
    • Every value is equally likely
    • The mean is one of the listed values
    • Tick every box that applies.

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

    Answer

  3. The Total

    A distribution has probabilities 0.2, 0.3 and one unknown. What must the third be?

    Answer

  4. The Mean

    Values 0, 1, 2 with probabilities 0.25, 0.5, 0.25. What is the mean?

    Answer