13.1.1. Random Variables: Discrete vs Continuous

Try these first

1. 1.

   What is a discrete random variable? Provide an example.

   Hint

   Think of variables that can be counted easily.

2. 2.

   What is one property of a PDF?

   Hint

   Think about the chances of probability being negative.

3. 3.

   What type of random variable can take on countable values?

   • Discrete Random Variable
   • Continuous Random Variable
   • Both

   Hint

   Think about whether the values can be counted.

4. 4.

   True or False: The total area under a PDF is always equal to one.

   • True
   • False

   Hint

   Consider how probabilities sum up across all outcomes.

5. 5.

   Given a PDF defined as f(x) = 1/3 for 0 ≤ x ≤ 3 and 0 otherwise, calculate P(1 ≤ X ≤ 2).

   Hint

   Use the integral of the PDF over the specified interval.

6. 6.

   For a continuous variable with mean μ and variance σ², derive the PDF for the normal distribution.

   Hint

   Consider the characteristics of normal distributions and their symmetrical properties.