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.
Warm-Up: Sample Spaces and Probabilities
These problems review sample-space ideas you already know.
Two fair coins are tossed; the sample space is HH, HT, TH, TT with each outcome equally likely. Let $X = $ the number of heads. Give for each outcome: $X(\text{HH}) = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , $X(\text{HT}) = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , $X(\text{TT}) = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .