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Original
2026-01-01
Modified
2026-02-28
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<p><strong>Variance of Binomial Distribution</strong></p>
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<p><strong>Variance of Binomial Distribution</strong></p>
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<p>The<a>binomial distribution</a>is a<a>discrete probability distribution</a>that represents the number of positive outcomes in a binomial experiment conducted n times, where each trial has only two possible outcomes: success (1) or failure (0). The<a>variance of a binomial distribution</a>, denoted as σ2, is calculated by the formula:</p>
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<p>The<a>binomial distribution</a>is a<a>discrete probability distribution</a>that represents the number of positive outcomes in a binomial experiment conducted n times, where each trial has only two possible outcomes: success (1) or failure (0). The<a>variance of a binomial distribution</a>, denoted as σ2, is calculated by the formula:</p>
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<p>\(σ^2 =np(1-p)\)</p>
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<p>\(σ^2 =np(1-p)\)</p>
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<p>Where n is the number of trials, p is the probability of success in each trial, and (1-p) represents the probability of failure. Additionally, np is the mean (expected value) of the binomial distribution, indicating the average number of anticipated successes in n trials.</p>
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<p>Where n is the number of trials, p is the probability of success in each trial, and (1-p) represents the probability of failure. Additionally, np is the mean (expected value) of the binomial distribution, indicating the average number of anticipated successes in n trials.</p>
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<p><strong>Variance of Poisson Distribution</strong></p>
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<p><strong>Variance of Poisson Distribution</strong></p>
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<p>The Poisson distribution is a discrete probability distribution used to model the likelihood of a certain number of events occurring within a fixed interval of time or space. It is characterized by the parameter λ (lambda), which represents both the mean and the variance of the distribution. In other words, for a Poisson distribution, the mean and variance are equal, and the formula gives the variance σ2:</p>
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<p>The Poisson distribution is a discrete probability distribution used to model the likelihood of a certain number of events occurring within a fixed interval of time or space. It is characterized by the parameter λ (lambda), which represents both the mean and the variance of the distribution. In other words, for a Poisson distribution, the mean and variance are equal, and the formula gives the variance σ2:</p>
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<p>\(σ^2 =λ\)</p>
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<p>\(σ^2 =λ\)</p>
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<p>Where λ indicates the average<a>rate</a>of event occurrences in the interval.</p>
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<p>Where λ indicates the average<a>rate</a>of event occurrences in the interval.</p>
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<p><strong>Variance of Uniform Distribution</strong></p>
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<p><strong>Variance of Uniform Distribution</strong></p>
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<p>The uniform distribution is a continuous probability distribution in which all outcomes within a specific interval, defined by the lower bound a and the upper bound b, are equally likely. Because of this equal probability for all values in the range, the uniform distribution is also called a rectangular distribution. The variance of a uniform distribution is calculated using the formula:</p>
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<p>The uniform distribution is a continuous probability distribution in which all outcomes within a specific interval, defined by the lower bound a and the upper bound b, are equally likely. Because of this equal probability for all values in the range, the uniform distribution is also called a rectangular distribution. The variance of a uniform distribution is calculated using the formula:</p>
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<p>\(σ^2 = \frac{(b-a)^2}{12}\)</p>
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<p>\(σ^2 = \frac{(b-a)^2}{12}\)</p>
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<p>and its mean is given by:</p>
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<p>and its mean is given by:</p>
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<p>\(Mean = \frac{(a+b)}{2}\)</p>
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<p>\(Mean = \frac{(a+b)}{2}\)</p>
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<p>Where ‘a' is the minimum value and 'b' is the maximum value of the distribution.</p>
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<p>Where ‘a' is the minimum value and 'b' is the maximum value of the distribution.</p>