How is the probability distribution function of a random variable with a standard normal distribution characterized?
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The probability distribution function of a random variable with a standard normal distribution is characterized by the fact that it is the only distribution for which the sample mean and variance are independent . This property is known as the Geary theorem. The standard normal distribution is also characterized by having a mean of zero and a variance of one. Additionally, the normal distribution is the only distribution for which the sum of a large number of independent variables is asymptotically distributed like a Gaussian distribution, as stated by the central limit theorem . The standard normal distribution is commonly used in engineering and scientific applications, and it is often represented by standardized random variables with means equal to zero and variances equal to one .
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| The probability distribution function of a random variable with a standard normal distribution is characterized by a mean of zero and a variance of one. | |
| The probability distribution function of a random variable with a standard normal distribution is characterized by a Gaussian distribution. | |
| The paper describes various characteristic constants and parameters for probability distributions, including the standard deviation for a random variable with a standard normal distribution. | |
| The probability distribution function of a random variable with a standard normal distribution is characterized by a bell-shaped curve. | |
Open access•Posted Content | The probability distribution function of a random variable with a standard normal distribution is characterized by the fact that the sample mean and variance are independent. |
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