13.1. Probability Density Function (PDF)

Try these first

1. 1.

   What is a PDF?

   Hint

   Think of how probabilities are represented for continuous outcomes.

2. 2.

   Is the probability of a continuous variable taking a specific value greater than zero?

   Hint

   Consider how probabilities are defined for intervals.

3. 3.

   What is a Probability Density Function?

   • A function for discrete outcomes
   • A function for continuous outcomes
   • Neither of the above

   Hint

   Remember the definitions of different types of functions.

4. 4.

   True or False: The probability of a continuous random variable taking a specific value is greater than zero.

   • True
   • False

   Hint

   Review how probabilities are defined.

5. 5.

   Given a PDF f(x) = 3x² for 0 ≤ x ≤ 1, verify that it is a valid PDF and find E[X].

   Hint

   Use integration techniques to confirm area and moments.

6. 6.

   If the variance is given by Var(X) = ∫ (x - E[X])² * f(x) dx, compute the Variance for f(x) = 1/5 for 0 ≤ x ≤ 5.

   Hint

   Remember to use integration for both components of variance calculation.