Probability and Statistics

The Discrete probability distribution and the continuous probability distribution are two types of probability distributions that define discrete and continuous random variables respectively. A probability distribution can be defined as a function that describes all possible values of a given random variable as well as its associated probabilities. Discrete Probability Distribution Definition The discrete probability […]

The probability of an event occurring is determined by probability. There are a variety of situations in which we must forecast the outcome of a real-life event. We may be certain or doubtful about the result of an event. In these situations, we say the event has a chance of happening or not happening. In

Total Probability is the sum of all possible outcomes from an event, and it can be calculated by adding up the probabilities of each outcome. For example, if you roll two dice, there are six possible outcomes: 1-2, 3-4, 5-6. The total probability for this roll would be 6/6 or 1. The rule of total probability is used to determine

These axioms, as stated below, are a reduced version of those proposed by mathematician Andrey Kolmogorov in 1933. The core concepts of probability theory had previously been “thought to be somewhat unique,” therefore his goal was to place them in their “natural home, among the general notions of modern mathematics.” To this purpose, Kolmogorov provided

We hear the term probability a lot, but we don’t appreciate how powerful it is. The probability, in simple terms, is the likelihood or chance of something happening. The Axioms of Probability, which are necessary for statistics and exploratory data analysis, are one of the core principles of probability. Axioms are rules or principles that

Statistics and probability are two mathematical terms that analyze the frequencies of any event. We generally predict the outcome of many cases or the likelihood of a particular consequence. We often determine the result of events by calculating their probability. Tossing a coin, for instance, has two possible outcomes: head or tail. There is no way

Logic is the study of how to think logically. For example, to prove a theorem, we need to know how to evaluate the validity of a given argument. Statement of operation A valid statement is a declarative phrase that is either true or untrue, but not both. Otherwise, it is referred to as an erroneous

The axioms are a reduced version of those proposed by mathematician Andrey Kolmogorov in 1933. The core concepts of probability theory had previously been “thought to be somewhat unique,” therefore his goal was to place them in their “natural home, among the general notions of modern mathematics.” To this purpose, Kolmogorov provided a mathematical explanation

The probability distribution of a random variable describes how probabilities are spread over the random variable’s values. The probability distribution of a discrete random variable, x, is characterised by a probability mass function, represented as f(x). This function gives back the chance that each random variable value is true. Two conditions must be met to

A random variable is a numerical representation of a statistical experiment’s outcome. A discrete random variable can only take one of two values: a finite number or an infinite succession of values; a continuous random variable can take any value in any interval on the real number line. A sample space is the collection of