7.1.2.1. Definition

Try these first

1. 1.

   Define a random variable.

   Hint

   Think about examples like coin flips.

2. 2.

   What does PDF stand for?

   Hint

   Consider the role of probability in measuring variability.

3. 3.

   What does PDF stand for?

   • Probability Distribution Formula
   • Probability Density Function
   • Probability Distribution Function

   Hint

   Think about how 'density' relates to probability.

4. 4.

   True or false: The area under a PDF curve must equal 1.

   • True
   • False

   Hint

   Consider how probability is distributed over an interval.

5. 5.

   A continuous random variable has a PDF given by f(x) = 3x² for 0 ≤ x ≤ 1. Calculate the probability that X is between 0.2 and 0.5.

   Hint

   Set up the integral carefully to find the area for the specified interval.

6. 6.

   Given a Gaussian PDF, determine the mean and variance if the PDF is defined as f(x) = (1/√(2πσ²)) e^(-(x-μ)²/(2σ²)).

   Hint

   Think about the defining parameters of the Gaussian distribution.