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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
In statistics, a standard normal table, also called the unit normal table or Z table, [1] ... If X is a random variable from a normal distribution with mean ...
This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [1] [2] In other words, () is the probability that a normal (Gaussian) random variable will obtain a value larger than standard deviations.
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. [1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability [ 2 ] but instead is a mathematical function in which
Then the random variables and are uncorrelated, and each of them is normally distributed (with mean 0 and variance 1), but they are not independent. [ 7 ] : 93 It is well-known that the ratio C {\displaystyle C} of two independent standard normal random deviates X i {\displaystyle X_{i}} and Y i {\displaystyle Y_{i}} has a Cauchy distribution .
A real random vector = (, …,) is called a centered normal random vector if there exists a matrix such that has the same distribution as where is a standard normal random vector with components. [ 1 ] : p. 454
The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable whose real and imaginary parts are independent normally distributed random variables with mean zero and variance /. [3]: p. 494 [4]: pp. 501 Formally,