But the amazing growth of our techniques, the adaptability and precision they have attained, the ideas and habits they are creating, make it a certainty that profound changes are impending in the ancient craft of the Beautiful.

Because the area under f is 1, the cumulative function ranges monotonically from 0 to 1. The variable, X, on the horizontal axis of a density function or the associated cumulative graph is called a random variable.

In practice, when we attempt to estimate a variable by assigning a range of possible values, we are in effect defining a random variable. Properly speaking, we have been discussing one of the two major classes of random variables—continuous ones.

Shortly, we introduce the notion of a discrete random variable, for which we have: Histograms Cumulative curves The interpretations of the statistics we have defined The reason to have both density functions and cumulative functions is that density functions help us identify the mode, the range, and the symmetry or asymmetry of a random variable.

In practice, cumulative functions answer questions like: What is the chance of losing money on this investment [i. How likely is it that the well will be drilled in less than 65 days?

Today, we enjoy a choice of software that, when supplied a given histogram, fits various probability distributions normal, log-normal, beta, triangular to it.

The curve that yields a minimum chi-square value is considered as the best fit.

Thus, we begin with data, construct a histogram, then find the best fitting curve, and assume that this curve represents the population from whence the data came.

We do this because, when we build a Monte Carlo simulation model, we want to sample hundreds or thousands of values from this imputed population and then, in accordance with our model i.

For instance, one way to estimate oil in place for an undrilled prospect is to: Use analogous data for net volume, porosity, oil saturation, and formation volume factor Fit a curve to each data set Sample a single value for each of these four variables and take their product.

This gives one possible value for the oil in place. We then repeat this process a thousand times and generate a histogram of our results to represent the possible oil in place.

Now that we have these graphical interpretations, we should extend our definitions of mean, mode, median, and standard deviation to them.

The mode of a histogram is generally defined to be the midpoint of the class having the highest frequency the so-called modal class. In case of a tie, when the two classes are adjacent, we use the common boundary for the mode.

When the two classes are not adjacent, we say the data or the histogram is bimodal. One can have a multimodal data set.

One problem with this definition of mode for a histogram is that it is a function of the number of classes.Time Value of Money The time value of money (TVM) or, discounted present value, is one of the basic concepts of finance and was developed by Leonardo Fibonacci in The time value of money (TVM) is based on the premise that one will prefer to receive a certain amount of money today than the same amount in the future, all else equal.

As a result, when one deposits money .

Whenever you need help with writing a powerful introduction, use one of these recommended essay hook sentences to grab reader’s attention.

Hooks are crucial for any type of academic paper. It is not about answering the question but engaging your reader and making them interested. The Good, the Bad and Vape Pen for Wax. Thus far, no longterm respiratory effects are all linked to employing wax pencil vaporizers.

Then you require something small In the event you are searching to get a pencil to shoot approximately everywhere.

Descriptive statistics should aid communication. As the name suggests, it is intended to develop and explain features of both data and probability distributions. The time value of money (TVM) is an important concept to investors because a dollar on hand today is worth more than a dollar promised in the future.

The dollar on hand today can be used to invest. Ah, but super-human AI is not the only way Moloch can bring our demise. How many such dangers can your global monarch identify in time? EMs, nanotechnology, memetic contamination, and all the other unknown ways we’re running to the bottom.

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