Section 5.8 Exercises
Here are some exercises to consider related to Probability Functions.
Checkpoint 5.8.1. Flipping A Fixed Number of Coins.
Consider the random variable from the previous section where you flip three coins and measure the number of heads obtained. Determine f(0), f(1), f(2), and f(3) and the corresponding distribution function F(x). These can be expressed in a table format. Generalize your answer to the case when you flip a n coins where n is a fixed natural number.
Checkpoint 5.8.2. Flipping Fixed Number of Coins.
You flip three coins and measure the number of heads obtained. Determine the space \(R\) for the corresponding random variable \(X\text{.}\) From the eight possible outcomes, determine all outcomes corresponding to \(X = 2\text{.}\) Identify the random variable as discrete or continuous.
Checkpoint 5.8.3. Flipping Coins till success.
You flip one coin repeatedly until you get a second head. Determine the space \(R\) for the corresponding random variable \(X\text{.}\) From the possibilities, determine all outcomes corresponding to \(X = 4\text{.}\) Identify the random variable as discrete or continuous.
Checkpoint 5.8.4. Time between Accidents.
Now you want to measure the time between accidents at a particular intersection in town. Determine the space \(R\) for the corresponding random variable \(X\text{.}\) Describe all outcomes corresponding to \(X \lt 1\text{.}\) Be purposeful in the problem to describe the units you are using to measure time. Identify the random variable as discrete or continuous.