The following course in Probability and statistics is provided in its entirety by Atlantic International University's "Open Access Initiative " which strives to make knowledge and education readily available to those seeking advancement regardless of their socio-economic situation, location or other previously limiting factors. The University's Open Courses are free and do not require any purchase or registration, they are open to the public.
The course in Probability and statistics contains the following:
The Administrative Staff may be part of a degree program paying up to three college credits. The lessons of the course can be taken on line Through distance learning. The content and access are open to the public according to the "Open Access" and " Open Access " Atlantic International University initiative. Participants who wish to receive credit and / or term certificate , must register as students.
Probability is used to quantify an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty), we call probability. Thus the higher the probability of an event, the more certain we are that the event will occur.
In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable. Objects of any of these types but involving more than one variable may be called multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.
Lesson 3: Summation
If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum (possibly by virtue of the convention for empty sums).
Lesson 4: Axioms and Theorems: Axiom vs Theorem
An axiom is a statement that is considered to be true, based on logic; however, it cannot be proven or demonstrated because it is simply considered as self-evident. Basically, anything declared to be true and accepted, but does not have any proof or has some practical way of proving it, is an axiom. It is also sometimes referred to as a postulate, or an assumption.
An axiom’s basis for its truth is often disregarded. It simply is, and there is no need to deliberate any further. However, lots of axioms are still challenged by various minds, and only time will tell if they are crackpots or geniuses.
Lesson 5: DISCRETE RANDOM VARIBLE
In probability and statistics, a random variable, aleatory variable or stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense). A random variable can take on a set of possible different values (similarly to other mathematical variables), each with an associated probability (if discrete) or a probability density function (if continuous), in contrast to other mathematical variables.
Lesson 6:NORMAL DISTRIBUTION
In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known.
Lesson 7:BIVARIATE DATA
Scatter plots: A scatter plot, scatterplot, or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data.
The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. This kind of plot is also called a scatter chart, scatter gram, scatter diagram, or scatter graph.
Lesson 8: Sampling and Experiments
In statistics, quality assurance, & survey methodology, sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Each observation measures one or more properties (such as weight, location, color) of observable bodies distinguished as independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly stratified sampling. Results from probability theory and statistical theory are employed to guide practice. In business and medical research, sampling is widely used for gathering information about a population.
Lesson 9: ESTIMATIONS
Margins of error and estimates: The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population. Margin of error occurs whenever a population is incompletely sampled.
Lesson 10: TESTS OF SIGNIFICANCE
In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variablecharacterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together.
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