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.
Fluency Practice
Build distributions by grouping outcomes by value and summing probabilities.
Two fair coins are tossed; each of the four outcomes HH, HT, TH, TT has probability . Let $X = $ the number of heads. List the possible VALUES of from least to greatest: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .