Suppose that you collected data on GPA and the number of studying hours(H) for 100 students
at UCR. The data is summarized as follows: 20 students study 6 hours a day and have a GPA of
2.0, 30 students study 6 hours a day and have a GPA of 4.0, 10 students study 10 hours a day and
have a GPA of 2.0, and 40 students study 10 hours a day and have a GPA of 4.0.
Please solve the following questions:

1. Find the join and marginal probabilities? ( hint: you may use a table with GPA and hours
   (H))
2. Find the probability of hours= 6 given that the GPA=2.0?
3. Find the probability of GPA=4 given hours = 10?
4. Find the mean or expected value of hours (E(H))?? Find the variance of hours (V(H))?
5. Find the mean or expected value of GPA (E(GPA))?? Find the variance of GPA
   (V(GPA))?
6. Find the covariance between hours and GPA ( Cov(H, GPA)? Are the GPA and hours of
   studying independent?
7. Find the coefficient of correlation between hours and GPA ( r(H, GPA))?
8. Find the expected value (mean) of hours given that the GPA=2.0 ? Find the variance of
   hours given that the GPA=2.0?
9. Find the expected value (mean) of GPA given that the hours= 10? Find the variance of
   GPA given that the hours=10?

Sample Solution

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