Practice Expectation And Covariance (14.6) - Joint Probability Distributions

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8 questions

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6 sample questions

Question 1.
Calculate the expectation for discrete variable X with values 4, 5, 6 and probabilities 0.1, 0.4, 0.5 respectively.
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Use the formula E[X] = Σx * P(X=x).
Question 2.
What does it mean if Cov(X,Y) = 0?
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Consider the relationship between correlation and covariance.
3Question 3.
What is the expectation of a random variable?
- Average value
- Highest value
- Lowest value
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Think about how we calculate averages.
4Question 4.
Is Cov(X,Y) positive, negative, or zero if X and Y are independent?
- Positive
- Zero
- Negative
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Consider the definition of independent variables.
Question 5.
Given the joint distribution P(X,Y) for X and Y, how do you determine if X and Y are independent?
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Review the independence formula.
Question 6.
For a dataset of heights and weights, calculate the correlation coefficient. Explain what it tells you about the relationship.
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Consider the meaning of ρ values in correlation.

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