6. Partial Differential Equations

Try these first

1. 1.

   What is a random variable?

   Hint

   Think about how outcomes get mapped.

2. 2.

   Name two examples of discrete random variables.

   Hint

   Consider countable outcomes.

3. 3.

   What does a discrete random variable represent?

   • Countable outcomes
   • Uncountable outcomes
   • Only continuous values

   Hint

   Think about how we categorize outcomes.

4. 4.

   True or False: A PMF can be used to model continuous random variables.

   • True
   • False

   Hint

   Recall the definitions of PMF and PDF.

5. 5.

   A factory produces light bulbs, with a 5% chance of each bulb being defective. If you randomly select 10 bulbs, model the number of defective bulbs as a binomial distribution. What is the expected number of defective bulbs?

   Hint

   Consider the probability of defectiveness for each bulb.

6. 6.

   A car's speed is modeled as a continuous random variable with PDF f(x) = kx for 0 ≤ x ≤ 2. Determine k and then find the CDF.

   Hint

   Use integration to derive the total area under the PDF.