Probability: event An event is an outcome for any experiment and it is denoted by a capital letter. It is the basic element to which probability is applied. When an experiment is performed, an event either happens, or it doesn’t. A simple event is denoted by a E with a subscript where the event is … Read more
Probability: Connections with the theories of earlier classes Nothing in life is certain and in all our activities, we gauge the chances of successful outcomes, from business to medicine to the weather. A probability helps in understanding a quantitative description of likelihoods associated with various outcomes. It helps in developing a bridge between descriptive and … Read more
Probability: Axiomatic (set theoretic) probability Given an experiment and a sample space, probability is used to designate each event A a number P(A), called the probability of the event A. This designation provides a precise measure of the chance that A will occur. To ensure that the probability assignments are consistent with the intuitive notions … Read more
Probability: mutually exclusive events Mutually exclusive events are called nonempty events which can be defined on the same sample space with each event while excluding the occurrence of the other.In other words, these events share no common elements. Mutually Exclusive Events There are several ways to express the concept of mutually exclusive, For instance, f … Read more
Probability: random experiments – exhaustive events When a sample space is divided into multiple mutually exclusive events where their union forms the sample space itself, then these events are called exhaustive events.A collectively exhaustive event contains all the possible elementary events for a certain experiment under consideration: In probability theory and logic, a set of … Read more
Probability: Occurrence of events: not, and, or events The event, E, is any subset of the sample space, S that is a set of outcomes which does not necessarily need to have all outcomes for random phenomena. The event, E, is said to have occurred if after the outcome is observed then the outcome lies … Read more
Probability: random experiments – sample spaces The sample space, S, for a random phenomenon is defined as the set of all possible outcomes. It is basically a list of unique, non-overlapping possible outcomes of random circumstances shown in a set representation denoted by symbol ‘S’. The outcomes must be mutually exclusive and exhaustive from each … Read more
Probability is a number of ways a certain event can occur to the number of possible outcomes. An outcome is one possible result of a probability and the act that leads to a single outcome that cannot be predicted with certainty is called an experiment. For instance, today there is a 45% chance of rain … Read more
Statistics – Analysis of frequency distributions with equal means but different variances The coefficient of variation is a measure of the relative variability (or consistency) of two or more data sets. It is calculated by taking the ratio of the standard deviation divided by the mean. It may also be expressed as a percentage to … Read more
Statistics – Measures of dispersion: Standard deviation Standard deviation (SD) is a measure of how each value in a data set varies or deviates from the mean. The standard deviation is calculated by deducing the square root of the variance. It is denoted with the same units as the original data. Assuming that all values … Read more