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Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years.
Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.
In the children's game rock, paper, scissors, two players simultaneously extend one hand in the form of a fist (rock), a flat palm (paper), or two fingers extended (scissors). If they both make the same choice, the game is a tie. Otherwise, rock beats scissors (because rock can crush scissors), scissors beats paper (because scissors can cut paper), and paper beats rock (because paper can cover rock). Whoever wins gains one point; in the case of a tie, no one gains any points. (a) Find the optimum strategy for each player and the value of the game. (b) In hindsight, how could you have guessed the answer to part (a) without doing any work?
Definition cumulative distribution function of :
is defined as the :
Take the natural logarithm of side of the inequality:
Use the power property of logarithms ):
The natural logarithm of is equal to 1:
Use the definition of the cumulative distribution function of :
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