Megawatts cht (in feet) 24 CHAPTER 2 Graphs and Functions Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. See Example 9. 218 89. 88. 87. (-2, 4) (-1, 3)+ 3. 2. (-3, 1), -2 -3 -2 -2- A (0, -2) (2,-4) (-2, -4) 92. 90. 91. (3, 1) (-2, 0) + (2, 0) ++ -3 0. 3 -2 (-3, –1) (0, –2)- (-1, –3) +(1, -3) (0, -4) Solve each problem. See Example 10. oto 93, Electricity Usage The graph shows the daily megawatts of electricity used on a record-breaking summer day in Sacramento, California. Electricity Use 2500 2300 2100 (a) Is this the graph of a function? 1900 1700 (b) What is the domain? 1500 (c) Estimate the number of megawatts 1300 1100 used at 8 A.M. 900 (d) At what time was the most electric- 700 х ity used? the least electricity? 12 Noon 16 20 (e) Call this function f. What is f(12)? Hours Interpret your answer. Source: Sacramento Municipal Utility District. (f) During what time intervals is increasing? decreasing? usage 94. Height of a Ball A ball is thrown straight up into the air. The function y = h(t) in the graph gives the height of the ball (in feet) at t seconds. (Note: The graph does not show the path of the ball. The ball is rising straight up and then falling straight down.) Height of a Thrown Ball 256 y = h(t) %3D 192 (a) What is the height of the ball at 2 sec? 128

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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.