7.1.1. Random Variables and Probability Distributions

Try these first

1. 1.

   What is a random variable?

   Hint

   Think of it as a representation of outcomes in numbers.

2. 2.

   Define a discrete random variable.

   Hint

   Consider examples like dice rolls or number of students.

3. 3.

   What is the normalization condition for a PDF?

   Hint

   Consider how probabilities relate to areas in geometry.

4. 4.

   True or false: CDF can give the probability of a random variable being greater than a specific value.

   • True
   • False

   Hint

   Think about what CDF shows and what it doesn't.

5. 5.

   A continuous random variable has a PDF defined as f(x) = kx for 0 ≤ x ≤ 2. Find the value of k and then the probability that X < 1.

   Hint

   Remember to normalize the PDF first, then use integration.

6. 6.

   The mean of a random variable X is defined by the integral μ = ∫ x f(x) dx. For the PDF f(x) = 2x (0 ≤ x ≤ 1), calculate the mean.

   Hint

   The integration step is crucial for finding the expected value!