14.6. Expectation and Covariance

Try these first

1. 1.

   Calculate the expectation for discrete variable X with values 4, 5, 6 and probabilities 0.1, 0.4, 0.5 respectively.

   Hint

   Use the formula E[X] = Σx * P(X=x).

2. 2.

   What does it mean if Cov(X,Y) = 0?

   Hint

   Consider the relationship between correlation and covariance.

3. 3.

   What is the expectation of a random variable?

   • Average value
   • Highest value
   • Lowest value

   Hint

   Think about how we calculate averages.

4. 4.

   Is Cov(X,Y) positive, negative, or zero if X and Y are independent?

   • Positive
   • Zero
   • Negative

   Hint

   Consider the definition of independent variables.

5. 5.

   Given the joint distribution P(X,Y) for X and Y, how do you determine if X and Y are independent?

   Hint

   Review the independence formula.

6. 6.

   For a dataset of heights and weights, calculate the correlation coefficient. Explain what it tells you about the relationship.

   Hint

   Consider the meaning of ρ values in correlation.