Back to Define a random variable and graph its distribution — Problem 1 · 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

Work through problems with immediate feedback

Warm-Up: Sample Spaces and Probabilities

These problems review sample-space ideas you already know.

Two fair coins are tossed, with sample space $\{$ HH, HT, TH, TT $\}$ . Let $X = $ the number of heads. Which statement correctly describes what $X$ does?

$X$ assigns a NUMBER to each outcome, e.g. $X(\text{HH}) = 2$ and $X(\text{TT}) = 0$ .

$X$ equals the outcome itself, e.g. $X = \text{HH}$ .

$X$ is the probability of getting heads, $\frac{1}{2}$ .

$X$ is the list of outcomes $\{$ HH, HT, TH, TT $\}$ .