Posted Mar 24, 2020 11:13 AM 1. P(x) = -x^3 + 3x^2 + 24x -3 decreases on (-infinity,-2). What does it do after that (to the right of -2 on the x-axis)? 2. What is the max of P(x) (y-value of its relative maximum point), and where is its min (x-value of its relative minimum point)? 3. Warning! At least one problem on the final exam will ask where the graph is smiling (concave up) or where the graph is frowning (concave down) or where the smile and the frown meet (inflection point). When this happens (and it will!) the plus signs and the minus signs on the number linç MUST BE DETERMINED BY THE SECOND DERIVATIVE (instead of the 1st). The 1st derivative of P(x) is -3x^2 + 6x +24. The 2nd is -6x + 6. So, based on the SECOND DERIVATIVE, my plus signs tell me that the graph is smiling (concave up) on (-infinity, ?). 4. Again, based on the SECOND DERIVATIVE, my minus signs tell me that the graph is frowning (concave down) on (?, infinity). 5. Where is the meeting place (inflection point) of the smile and the frown? REMINDER! Please answer all 5 questions in one very important email =) DE
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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