Lesson plan
Q-function
In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard deviations. Equivalently, Q(x) is the probability that a standard normal random variable takes a value larger than x . If Y is a Gaussian random variable with mean \mu and variance \sigma^2 , then X = \frac{Y-\mu}{\sigma} is standard normal and : P(Y > y) = P(X > x) = Q(x) where x = \frac{y-\mu}{\sigma} . Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally. Because of its relation to the cumulative distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics.
Article summary
In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard deviations. Equivalently, Q(x) is the probability that a standard normal random variable takes a value larger than x . If Y is a Gaussian random variable with mean \mu and variance \sigma^2 , then X = \frac{Y-\mu}{\sigma} is standard normal and : P(Y > y) = P(X > x) = Q(x) where x = \frac{y-\mu}{\sigma} . Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally. Because of its relation to the cumulative distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.