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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 ...
This is a list of probability topics. It overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals.
Probability of a random day of the year being your birthday (for all birthdays besides Feb. 29) 4×10 −3: Probability of being dealt a straight in poker 10 −2: Centi-(c) 1.8×10 −2: Probability of winning any prize in the UK National Lottery with one ticket in 2003 2.1×10 −2: Probability of being dealt a three of a kind in poker 2.3× ...
In probability theory, for a probability measure P on a Hilbert space H with inner product , , the covariance of P is the bilinear form Cov: H × H → R given by C o v ( x , y ) = ∫ H x , z y , z d P ( z ) {\displaystyle \mathrm {Cov} (x,y)=\int _{H}\langle x,z\rangle \langle y,z\rangle \,\mathrm {d} \mathbf {P} (z)}
Histogram derived from the adapted cumulative probability distribution Histogram and probability density function, derived from the cumulative probability distribution, for a logistic distribution. The observed data can be arranged in classes or groups with serial number k. Each group has a lower limit (L k) and an upper limit (U k).
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
A typical statistics course covers descriptive statistics, probability, binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation. [68] Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of free statistics ...