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:

- Find the join and marginal probabilities? ( hint: you may use a table with GPA and hours

(H)) - Find the probability of hours= 6 given that the GPA=2.0?
- Find the probability of GPA=4 given hours = 10?
- Find the mean or expected value of hours (E(H))?? Find the variance of hours (V(H))?
- Find the mean or expected value of GPA (E(GPA))?? Find the variance of GPA

(V(GPA))? - Find the covariance between hours and GPA ( Cov(H, GPA)? Are the GPA and hours of

studying independent? - Find the coefficient of correlation between hours and GPA ( r(H, GPA))?
- Find the expected value (mean) of hours given that the GPA=2.0 ? Find the variance of

hours given that the GPA=2.0? - 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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