17.1. Random Variables – A Quick Recap

Try these first

1. 1.

   Define a discrete random variable and give an example.

   Hint

   Think about counts or finite values.

2. 2.

   What is a continuous random variable?

   Hint

   Consider things that can vary infinitely.

3. 3.

   What is the definition of a random variable?

   • A fixed value in statistics
   • A function assigning real numbers to outcomes
   • An uncountable set of outcomes

   Hint

   Remember, it relates to outcomes of uncertainty.

4. 4.

   Two random variables are considered independent if:

   • True
   • False

   Hint

   Think about the impact of one variable on another.

5. 5.

   Suppose you have two discrete random variables, A and B, with the following probabilities: P(A=1)=0.4, P(A=2)=0.6, P(B=1)=0.5, P(B=2)=0.5. Verify if A and B are independent if P(A=1, B=1)=0.2.

   Hint

   Use the independence condition to verify.

6. 6.

   In a continuous scenario, if the joint probability density function for X and Y is f(x, y) = e^(-x) * e^(-y) for x,y>0, analyze the independence of X and Y.

   Hint

   Express the joint PDF in terms of marginal PDFs.