6.5. Comparison Table

Try these first

1. 1.

   Define a discrete random variable with an example.

   Hint

   Think of a situation where you can count specific outcomes.

2. 2.

   What is a continuous random variable? Provide one example.

   Hint

   Consider measurements that are not limited to whole numbers.

3. 3.

   What is the key characteristic of discrete random variables?

   • They take countable values
   • They take uncountable values
   • They cannot be measured

   Hint

   Remember the distinction between countable and uncountable outcomes.

4. 4.

   True or False: Continuous random variables use PMF.

   • True
   • False

   Hint

   Consider the type of functions used for each type of random variable.

5. 5.

   A coin is tossed three times. Define a discrete random variable for the number of heads obtained and calculate its PMF.

   Hint

   Use combinations for heads in this case.

6. 6.

   Given a continuous random variable with a PDF defined as f(x) = 3x^2 for 0 ≤ x ≤ 1, find the probability that the variable falls between 0.5 and 1.

   Hint

   Evaluate the integral at the limits provided.