Now Try Exercise 93. xercises CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. 1. The domain of the relation {(3, 5), (4, 9), ( 10, 13)} is 2. The range of the relation in Exercise 1 is 3. The equation y = 4x – 6 defines a function with independent variable and dependent variable 4. The function in Exercise 3 includes the ordered pair (6, –). 5. For the function f(x) = -4x + 2, ƒ(-2) = %3D 6. For the function g(x) = Vx, g(9) = %3D 7. The function in Exercise 6 has domain 8. The function in Exercise 6 has range У 9. The largest open interval over which the function graphed here increases is (3, 1) 10. The largest open interval over which the function graphed here decreases is 3. bnoqasn (8) To Decide whether each relation defines a function. See Example 1. 12. {(8,0), (5, 7), (9, 3), (3, 8)} 11. {(5, 1), (3, 2), (4, 9), (7, 8)} 14. {(9, -2), (-3, 5), (9, 1)} 13. {(2, 4), (0, 2), (2, 6)} of 16. {(-12, 5), (-10, 3), (8, 3)} 15. {(-3, 1), (4, 1), (-2, 7)} 3) 41 1012 2. 10 Decide whether each relation defines a function, and give the domain and range. See Examples 1-4. 19. {(1, 1), (1,-1), (0, 0), (2, 4), (2, –4)} 20. {(2, 5), (3, 7), (3, 9), (5, 11)} 21. 22. 10 21 15 11 17 3- 3. 19 27 20 23. 24. x -1 -2 2 -2 26. Attendance at NCAA Women's 25. Number of Visits to U.S. National Parks College Basketball Games Season* Attendance Number of Visits (y) (millions) Year (x) (x) (y) 2010 64.9 2011 11,159,999 2011 63.0 2012 11,210,832 2012 65.1 2013 11,339,285 2013 63.5 2014 11,181,735 Source: NCAA. Source: National Park Service. *Each season overlaps the given year with the previous year. 29. 27) ( (28. 2 -2- х -3 32. 31. 30. -3- 4. -4 4. -3 -3.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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