Problem (2): Sometimes we need to apply more than one technique to evaluate an integral. We will look at such a situation in this problem. .3 (a) The definite integral 9 - x2 dx computes the area of a vertically simple region R in the ry-plane. Sketch the region R and describe R as a vertically simple set. Be sure to label all axes, curves and any points of intersection. (b) Recall that definite integrals can be computed using a limit of a Riemann sum, geometry, or the Fundamental Theorem of Calculus. Explain in 1-2 sentences which method of evaluation is most V9- x2 dx and then use it to evaluate this definite integral. efficient for the definite integral (c) As mentioned at the beginning of this problem, some integrals will need a combination of two or xV9 - x4 dx. While this more methods in order to evaluate them. Consider the definite integral integral looks different from the integral in parts (a) and (b), the right substitution will show us it is IV9 - x4 dx into an very similar. Find a substitution that will transform the definite integral V3 V9 - x2 dx, and then evaluate equivalent definite integral that is related to xV9 - x4 dx. 9- (In x)2 rea (d) Evaluate dx.
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.
Problem 2 Parts A, B, and c please
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