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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
For example, if the event is "occurrence of an even number when a dice is rolled", the probability is given by =, since 3 faces out of the 6 have even numbers and each face has the same probability of appearing. Modern definition: The modern definition starts with a finite or countable set called the sample space, which relates to the set of ...
For any pair of positive integers n and k, the number of k-tuples of non-negative integers whose sum is n is equal to the number of multisets of size k − 1 taken from a set of size n + 1, or equivalently, the number of multisets of size n taken from a set of size k, and is given by
This is the definition of a probability density function, so that absolutely continuous probability distributions are exactly those with a probability density function. In particular, the probability for X {\displaystyle X} to take any single value a {\displaystyle a} (that is, a ≤ X ≤ a {\displaystyle a\leq X\leq a} ) is zero, because an ...
The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
Offset applied for CBSE Class 12 exams (Delhi) [21] [0 = no moderation] Subject Offset (2019) Offset (2018) Offset (2017) Offset (2016) Mathematics 11 9 10 15 Physics 11 9 9 8 Chemistry 10 9 9 7 Biology 5 0 3 0 Political Science 6 0 5 5 Economics 5 0 3 6 Business Studies 5 6 6 11 Sociology 2 0 0 6 Geography 1 0 0 8
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information " (in units such as shannons ( bits ), nats or hartleys ) obtained about one random variable by observing the other random ...