13.. Partial Differential Equations

Try these first

1. 1.

   Define a Probability Density Function (PDF).

   Hint

   Think about how we express probabilities for continuous variables.

2. 2.

   What is the definition of non-negativity in the context of PDFs?

   Hint

   Consider the graphical representation of a PDF.

3. 3.

   What describes the likelihood of a continuous random variable taking on a particular value?

   • Probability Mass Function
   • Probability Density Function
   • Cumulative Distribution Function

   Hint

   Think about continuous random variables.

4. 4.

   The total area under a PDF curve equals what?

   • True
   • False

   Hint

   Consider how probabilities relate to areas.

5. 5.

   A continuous random variable X follows a PDF given by f(x) = 2x for 0 ≤ x ≤ 1. Calculate the expected value E[X] and the variance Var(X).

   Hint

   Set up your integrals carefully and simplify appropriately.

6. 6.

   Given a normal distribution with mean μ = 0 and variance σ² = 1, compute the probability that a value lies between -1 and 1 using the standard normal table.

   Hint

   Consider how the area under the curve represents probabilities.