The random variables ? " W " " n " are independent and identically distributed normal random variables with expected value zero and variance \ Delta t.
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Circular symmetric complex normal random variables are used extensively in signal processing, and are sometimes referred to as just "'complex normal "'in signal processing literature.
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The "'polar method "'( attributed to George Marsaglia, 1964 ) is a pseudo-random number sampling method for generating a pair of independent standard normal random variables.
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A given data point is assigned a value which is either exactly, or an approximation, to the expectation of the order statistic of the same rank in a sample of standard normal random variables of the same size as the observed data set.
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Alternatively, since a half-normal distribution is always positive, the one bit it would take to record whether a standard normal random variable were positive ( say, a 1 ) or negative ( say, a 0 ) is no longer necessary.
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This method of producing a pair of independent standard normal variates by radially projecting a random point on the unit circumference to a distance given by the square root of a chi-square-2 variate is called the polar method for generating a pair of normal random variables,
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If we wish to test the hypothesis that the population odds ratio equals one, the two-sided p-value is / SE ) } }, where " P " denotes a probability, and " Z " denotes a standard normal random variable.
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In probability theory, the "'Rice distribution "', "'Rician distribution "'or "'Ricean distribution "'is the probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean.
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In math we often "-ize " things when we transform them to a more convenient or easily comparable form ( e . g . " normalizing " a vector so it has unit length, " standardizing " a normal random variable so it has mean 0 and SD 1 ).
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:Logarithms do a few useful things-they turn multiplicative relationships into additive ones, they turn a log-normal random variable into a normal one, and they take things which are centred about 1 and make them centred about 0, which in some circumstances can make analysis easier ( the first two properties are more useful than the third ).
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