6.6. Summary

Try these first

1. 1.

   Define a random variable.

   Hint

   Think about what a random experiment is.

2. 2.

   What is a discrete random variable?

   Hint

   Consider examples like rolling dice or coin tosses.

3. 3.

   What type of random variable can take on a countable number of values?

   • Continuous Random Variable
   • Discrete Random Variable
   • Both

   Hint

   Recall the definitions of each type.

4. 4.

   True or False: The total probability across all values for a PMF sums to 1.

   • True
   • False

   Hint

   Think about the definition of probability for random variables.

5. 5.

   A factory produces lightbulbs with a probability of 0.02 being defective. Let X be the number of defective lightbulbs in a batch of 100. Model X and determine its PMF.

   Hint

   Relate the problem to a binomial scenario with trials.

6. 6.

   A continuous random variable X has a distribution defined from a PDF of f(x) = 4x for 0 < x < 0.5. Calculate the expected value E(X).

   Hint

   Set up the integral for the expected value using the PDF.