14.5. Independence of Random Variables

Try these first

1. 1.

   Define independence of random variables.

   Hint

   Think about how one variable's outcome impacts another.

2. 2.

   Given P(X=2) = 0.3, P(Y=3) = 0.5, calculate P(X=2, Y=3) if X and Y are independent.

   Hint

   Use the formula for the joint probability of independent events.

3. 3.

   What is the definition of independence in probability?

   Hint

   Consider the influence one variable has over another.

4. 4.

   If P(X=1) = 0.4 and P(Y=2) = 0.6, what is P(X=1, Y=2) if X and Y are independent?

   • 0.24
   • 0.10
   • 0.20

   Hint

   Multiply the individual probabilities of X and Y.

5. 5.

   A fair die is rolled twice. What is the probability of rolling a two on the first roll and a three on the second? Are these events independent?

   Hint

   Use the independence formula for joint probabilities.

6. 6.

   If X and Y are independent random variables with P(X=1) = 0.2 and P(Y=1) = 0.5, what is P(X=1, Y=1)? Are they independent?

   Hint

   Apply the independence condition to find joint probabilities.