3. Find the length of the function of r over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. y = x*/3 from (1, 1/3) to (3, 3) %3D
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.
![1. Find the volume V of the solid generated by revolving the region bounded by the
graphs of f(r) = x² and g(r)= 12 – r to the right of r = 1 about the y-axis.
2. Find the volume V of the solid of revolution generated by revolving the region bounded
by the graph of y = 2x – 2x and the x-axis about the line a = 2
3. Find the length of the function of a over the given interval. If you cannot evaluate the
integral exactly, use technology to approximate it.
y = x*/3 from (1, 1/3) to (3,3)
4. Let f(r) = r over the interval (0, 1]. Findthe surface area of the surface generated
by revolving the graph of f(x) around the x-axis. If you cannot evaluate the integral
exactly, use your calculator to approximate it.
5. Use the Pappus Theorem to find the volume of the solid formed by revolving the region
enclosed by the circle (r - 3)² + y² = 1 about the y-axis.
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