Using the probabilities the variance of x represented by Var(x) is equal to var(X) = E(X²) – [E(X)]² , where E(x) represents the expected value of x.
Given the probabilities of the random variable given by x₁ , x₂ , x₃ ,... has the probabilities of P₁ , P₂ , P₃ ...
We know that Variance is given by the formula:
[tex]Var(x) = \sigma^2=\sum_{i=1} ^n (x_i-\mu)^2px_i)\\\\=\sum_{i=1} ^n(x_i^2-2x_i+\mu^2)\\\\=E(x^2)-[E(x^2)][/tex]
We know that expected value is denoted by E(x) .
Hence the variance is denoted by var(X) = E(X²) – [E(X)]² .
In probability theory and statistics, variance is the predicted squared deviation of a random variable from its population mean or sample mean.
The scattering, or how far apart from the mean a bunch of data are from one another, is measured by variance. A few ideas that involve variance are descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
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