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When considering the probability of two different events or outcomes, it is essential to clarify whether they
are mutually exclusive or independent. If the events are mutually exclusive, then the probability that either
one or the other will occur equals the sum of their individual probabilities. This is known as the law of
addition.
If, however, two or more events or outcomes are independent, then the probability that both the first and
the second will occur equals the product of their individual probabilities. This is known as the law of
multiplication.
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What is the additional and multiplication theorems?
plz answer me
What is the relationship between statistical inference and probability theory and how do I support it with examples?
Probability theory is the field of mathematics that enables statistical inferences to be made. All equations used in statistical inferences must be based on mathematics (theorems and proofs) of probability theory. An example to illustrate this. Given a normal probability curve with a mean = 0 and variance of 1, 68% of the area under the curve is in the range of -1 to 1, as calculated from probability theory. Since it is proved by mathematics, we can state it as a fact. If we collect data, and the average of the data is zero, and the standard deviation is 1, then we can infer that we are 68% certain that the population mean lies between -1 to 1. Our conclusion is inferred based on our limited and imperfect sample and the assumption that our population is normally distributed.
Is being an actuary boring?
It really depends on the individual to be honest. I currently a trainee actuary looking to take on a different career path as I do find the job quite dull. 90% of my time is spent looking a spreadsheets and the exams which I'm studying for (which are extremely time consuming and generally reduce your social life) have little or nothing at all to do with my day to day job. I often believe that learning probability and other complex mathematical theorems for exams is very necessary and just a method of screening out those who aren't fully committed to obtaining final Actuarial qualification. That being said if you do enjoy studying maths then this is a solid career path which guarantees you (once qualified) to a well paid and relatively low pressure job. Everyone is different so I encourage other maths graduates to give the career a try if interested and simply move like myself if you find it dull.
Is it possible to doubt everything or almost everything?
It's often less difficult and requires less effort to doubt rather than to believe. It requires less thinking, rationalization, and research to doubt a subject than it would to do the necessary steps to bring one to raw belief. In order to doubt, only a few factors must be considered. However, in order to reach pure belief, many factors, theorems, and proofs must be presented. And, still, if one is leaning toward non-belief, it is difficult to separate the salient points that led you not to believe against the other side of the debate that would instill in you a true belief.
What is statistics as numerical facts?
Your question is very broad, but I will attempt to answer it, without entering into a philosophical question of statistics vs. facts. I have attached to related links. Sometimes a simple question does not have a simple answer. This is one of them. The term "fact" may have different meanings depending the context in which it is used. Facts may be different when they are: 1) Legal 2) Historical 3) Mathematical and 4) Scientific. The focus of this discussion is scientific facts verses statistics. Legal: Usually the "facts of a case" are elements of a legal case which neither party contests. This discussion does not relate to the use of facts as a legal term. Mathematics: An idea is a conjecture before it is proved, and then it becomes a proved theorem. The laws of addition, multiplication, etc are rigorously established. I can say, it is a fact that 2+2 = 4. This discussion of facts does not relate to the mathematical use of the words proof, theorems, laws or facts. Historical: Events which are witnessed by many and recorded are historical facts. Scientific facts: Relates to certain phenomena that is so well established, like the force of gravity, that scientists consider there is a natural law of gravity. The equations governing many natural phenomena have numerical constants. Now, statistics resulting from the collection of data assists in the scientific study of phenomena or processes. If certain physical numerical constants are identified through scientific study and approximated by reliable statistics through observations or experiments that can be duplicated by others, they may be considered "known constants"- which I would prefer to "numerical facts." Sometimes, our known facts change with more data- like the mass of some of our planets. Why is this important? Certain branches of science like physics and chemistry can through controlled experimentation identify physical constants. However, in other branches of science, like environmental science, the physical mechanisms are complex and measurement data is both scarce and variable. In these cases, science is advanced a combination of reliable statistics and known physical constants. You may want to investigate more on areas like global warming, ozone depletion or many social problems to identify statistics verses known physical constants.
What is the additional and multiplication theorems?
plz answer me
What are the geometry theorems in tenth grade geometry?
Here are some examples of 10th-grade geometry theorems: https://quizlet.com/subject/geometry-10th-grade-theorems/
What has the author Ryszard Jajte written?
Ryszard Jajte has written: 'Strong limit theorems in noncommutative L2-spaces' -- subject(s): Ergodic theory, Limit theorems (Probability theory), Limit theorems (Probabilitytheory), Von Neumann algebras
What has the author T V Arak written?
T. V. Arak has written: 'Uniform limit theorems for sums of independent random variables' -- subject(s): Distribution (Probability theory), Limit theorems (Probability theory), Random variables, Sequences (Mathematics)
What are the theorems on Differentiation of Algebraic Functions and its examples?
Subjective part of science
What has the author Richard Ronald Eakin written?
Richard Ronald Eakin has written: 'Some theorems on the two-sample problem' -- subject(s): Distribution (Probability theory)
How many theorems is Pythagoras responsible for?
6 theorems
When was Some theorems on artificial selection created?
Some theorems on artificial selection was created in 1934.
Is theorems accepted without proof in a logical system in geometry?
No, theorems cannot be accepted until proven.
What is problem solving skills?
Problem solving skills are skills that are needed to solve problems, such as research skills, being able to think and reason clearly, etc.In math, problem solving skills include being able to select whether to use addition, subtraction, multiplication, or division for word problems, knowing how to add, subtract, multiply, and divide, knowing basic theorems, and much more.
Can algebra properties be used as a reason in a proof?
Yes; In fact, I have found that they are necessary to finish most proofs. I started geometry a couple weeks ago, and so far I have used the Properties of Addition, Subtraction, Multiplication, and Division, the Partition Property, the Reflexive Property, and the Transitive and Substitution Properties. (Not sure if that's all of the algebra properties or not!) Postulates & theorems just aren't enough to solve a lot of problems.
What is the relationship between statistical inference and probability theory and how do I support it with examples?
Probability theory is the field of mathematics that enables statistical inferences to be made. All equations used in statistical inferences must be based on mathematics (theorems and proofs) of probability theory. An example to illustrate this. Given a normal probability curve with a mean = 0 and variance of 1, 68% of the area under the curve is in the range of -1 to 1, as calculated from probability theory. Since it is proved by mathematics, we can state it as a fact. If we collect data, and the average of the data is zero, and the standard deviation is 1, then we can infer that we are 68% certain that the population mean lies between -1 to 1. Our conclusion is inferred based on our limited and imperfect sample and the assumption that our population is normally distributed.
