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Symmetric distribution for continuous probability distribution, specifically standard normal distribution, showcasing its perfect symmetry about the mean (0).A symmetric discrete distribution, specifically a binomial distribution with 10 trials and a success probability of 0.5.
In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.
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