Probability in Other fields

1. For starts in finance we are often trying to predict the values and prices of uncertain future events and easy to understand event is option pricing before we proceed we need to understand what an option is and how we determine its price. So an option is an agreement between two parties for the price of a stock or item at a future point in time. It is called that way because it allows one of the sides to decide whether to go through with the deal at a later date. Since this pact puts one of the parties at a clear disadvantage the other one must pay them a compensation fee called the premium. Essentially whoever pays the premium gets to decide if the deal is going to go through when the predetermined point in the future arrives. The pricing aspect of this option represents how much we are willing to pay to receive that pact or what the highest premium we would agree to is.
2. The term statistics is the sample equivalent of characteristics for a population dataset. If we somehow managed to record the eye color of everybody in the entire world and 65 percent are brown. That is a characteristic of the human population. However, if we make the plausible and much more reasonable choice of looking at maybe 1000 people then if 60% of them are brown eyed that is statistic. Statistics focuses predominantly on samples and incomplete data. Doing so bring some uncertainty to any of the results we reach. This uncertainty is what leads us to rely on some of the most important concepts of probability like expected values or prediction intervals. In a way, probability lays the groundwork for statistics because it defines terms like mean, variance or expected value. Statistics tries to analyze numeric and categorical data and see how well it resembles any of the probability distribution. Statistics introduces many useful concepts based on probability theory. A confidence interval of CI use uses sample data to define a range with an associated degree of certainty. These degrees of certainty are usually 90%, 95% or 99% and expressed the likelihood of the population mean being within that interval a more handwaving explanation of confidence intervals is that they simply approximate some margins for the mean of the entire population based on a small sample to calculate these confidence intervals. To calculate these CIs we must know: mean, variance and standard deviation are. A hypothesis is an idea that can be tested. Three crucial requirements for hupothesis testing are knowing the mean, variance and type of the distribution with the help of these three and some formulas. We can validate similar statements again to a specific degree of certainty. In the statistics fielf, we are often provided some sample data without explicitly being told what type of distribution it follows. We usually determine that on our own based on the shape of the curve and certain characteristics of the data just like when we were buying a new sweater we might think one of them is a good match but we can’t be sure until we test it. For starters any distribution we try on predicts a value for all points within our dataset. This is what the distribution anticipates the actual data point to be. So it is essentially a type of anticipated average value. Knowing the Type of a Distribution: create different models for computationally expensive and computer software which called this entire process mathematical modelling. Mathematical modeling is essentially an extension of statistics that data scientists deal with.
3. Data analysis usually try to analyze past data and use some insight we find to make reasonable predictions about the future. Furthermore in mathematical modeling we often tend to run artificial simulations to see how well our predictions match up to various possible future outcomes. Once such approach is called a Monte Carlo simulation. What a Monte Carlo simulation consists of we generate artificial data with which to test the predictive power of our mathematical models usually the data is not completely arbitrary but rather follows certain restrictions. Monte Carlo simulation: we can tweak restrictions, many models look well when we train them and perform poorly with new data. Data Science is an expansion of probability, statistics, and programming that implements computational technology to solve more advanced questions even when using it to predict future outcomes.