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Show that the two random variables of Exercise 102 are not independent.
Exercise 102
A certain college gives aptitude tests in the sciences and the humanities to all entering freshmen. If X and Y are, respectively, the proportions of correct answers that a student gets on the tests in the two subjects, the joint probability distribution of these random variables can be approximated with the joint probability density
What are the probabilities that a student will get
(a) less than 0.40 on both tests;
(b) more than 0.80 on the science test and less than 0.50 on the humanities test?
What is the probability that 10 hurricanes reach landfall in the strike area? What is the probability at least one of 10 hurricanes reaches land outside the strike area?
Calculate and plot lift, given a set of data, and analyze optimal policy. Analyze the data to determine the optimal policy for enhancing profitability.
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A producer of pleasure boats wants to maximize revenue during the next month. Two types of boats are sold, x1 and x2. Type x1 sells for $40,000 and type x2 sells for $30,000.
Produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.
Report a table of marginal means for each level of each of the three factors.
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The amount of a brand of soda in 12-ounces can is approx. normal with a mean of 12.1 ounces and a standard deviation of 0.15 ounces.
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