Independent identically-distributed random variables
Independent identically-distributed random variables In probability theory, a sequence ... or other collection of random variables is independent and identically distributed (i.i.d.) if each ...
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Redundant array of independent disks/Temp
Redundant array of independent disks/Temp In computing, a redundant array of independent disks (more commonly known as a RAID ... server computers, and is usually implemented with identically-sized disk drives. With decreases in hard ... also used the term, "Inexpensive" instead of "Independent") suggested a number of prototype "RAID Levels ... RAID. Similarly, the change from "Inexpensive" to "Independent" confuses many as to the intended ...
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Normal distribution
... in 1872 for a bivariate normal with independent components. The name "normal distribution" was coined ... sim N(\mu_Y, \sigma^2_Y) are independent normal random variables, then: Their sum is normally distributed with $U\; =\; X\; +\; Y\; \backslash sim\; N\; ...\; 2\_Y)$ (proof). Their difference is normally distributed with $V\; =\; X\; -\; Y\; \backslash sim\; N\; ...\; U$ and $V$ are independent of each other. If $X\; \backslash \; ...$
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Normal distribution (Psychology wiki)
... in 1872 for a bivariate normal with independent components. The name "normal distribution" was coined ... sim N(\mu_Y, \sigma^2_Y) are independent normal random variables, then: Their sum is normally distributed with $U\; =\; X\; +\; Y\; \backslash sim\; N\; ...\; 2\_Y)$ ( proof ). Their difference is normally distributed with $V\; =\; X\; -\; Y\; \backslash sim\; N\; ...\; U$ and $V$ are independent of each other. If $X\; \backslash \; ...$
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Probability-generating function
... identical probability-generating functions, then they are identically distributed. 3. The normalization of the probability density ... G'(1-)\right ]^2. Functions of independent random variables Probability-generating functions are particularly useful for dealing with functions of independent random variables. For example: If X 1 ... 2 , ..., X n is a sequence of independent (and not necessarily identically distributed) random ...
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De Finetti's theorem
... theorem explains why exchangeable observations are conditionally independent given some (usually) unobservable quantity to which ... is that frequentists often treat observations as independent that Bayesians treat as exchangeable. A Bayesian ... weaker than the assumption that they are independent and identically distributed. A random variable X has a ...
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Negative binomial distribution
... precisely the mass function of a Poisson distributed random variable with Poisson rate λ. In ... failures and successes in a series of independent and identically distributed Bernoulli trials. Specifically, for k+r Bernoulli ... of trials is a (displaced) negative-binomially distributed random variable. The number of failures ...
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Central limit theorem
... the fact that any sum of many independent identically distributed random variables will tend to be distributed according to a particular "attractor distribution". The ... variance, then it will be approximately normally distributed. Since many real processes yield distributions ...
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Renewal theory
... integers (usually starting at zero) which has independent identically distributed holding times at each integer $i$ (exponentially distributed) before advancing (with probability 1) to the ... S_2 , \ldots be a sequence of independent identically distributed random variables such that < ...
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Exponential distribution
... the following examples which yield approximately exponentially distributed variables: the time until you have your ... the system) are often modeled as exponentially distributed variables. The length of a process that ... thought of as a sequence of several independent tasks is better modeled by a variable ... distribution (which is a sum of several independent exponentially distributed variables). Reliability theory and reliability engineering ...
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