Back to Define a random variable and graph its distribution — Problem 2 · Task Set 27

Exercises: Define a Random Variable and Graph Its Probability Distribution

Work through each section in order. A random variable X is a rule that assigns a NUMBER to each outcome in a sample space. To build its probability distribution, group the outcomes by the value of X and add the probabilities in each group; the probabilities of all values must sum to 1. Write probabilities as fractions or decimals. For explanation problems, use complete sentences. Do NOT compute expected value — that comes next lesson.

Grade 11·19 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-md-a-1

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Warm-Up: Sample Spaces and Probabilities

These problems review sample-space ideas you already know.

A fair die is rolled and the sample space is $\{1, 2, 3, 4, 5, 6\}$ , each outcome equally likely. What must be true of the probabilities of all six outcomes?

They are each $\frac{1}{6}$ and they sum to $1$ .

They are each $\frac{1}{6}$ and they sum to $6$ .

They are each $1$ , since every face can appear.

They cannot be found without rolling the die many times first.