“uniform distribution”的概念、定义、翻译、参考文献-科学参考

uniform distribution

Mathematics

The uniform distribution on the interval [a,b] is the continuous probability distribution whose probability density function f is given by f(x) = 1/(b − a), where a ≤ x ≤ b. It has mean (a + b)/2 and variance (b − a)²/12. There is also a discrete form: on the set 1, 2, …, n, it is the probability distribution whose probability mass function is given by Pr(X = r) = 1/n, for 1 ≤ r ≤ n. For example, the random variable for the winning number in a lottery has a uniform distribution on the set of all the numbers entered in the lottery.

Economics

A discrete uniform distribution is described by the probability function P[X = x_i] = 1/N, where the random variable X can take values x₁,…, x_N. A continuous uniform distribution is described by the probability density function f_X(x) = 1/(b − a) where random variable X can take values x ∈ [a,b], and by the moment generating function $M (t) = \frac{e x p (b t) - e x p (a t)}{t (b - a)}$ for $t \neq 0$ . The mean of continuous uniform distribution is (b−a)/2 and the variance is (b−a)²/12.

单词	uniform distribution
释义	uniform distribution Mathematics The uniform distribution on the interval [a,b] is the continuous probability distribution whose probability density function f is given by f(x) = 1/(b − a), where a ≤ x ≤ b. It has mean (a + b)/2 and variance (b − a)²/12. There is also a discrete form: on the set 1, 2, …, n, it is the probability distribution whose probability mass function is given by Pr(X = r) = 1/n, for 1 ≤ r ≤ n. For example, the random variable for the winning number in a lottery has a uniform distribution on the set of all the numbers entered in the lottery. Economics A discrete uniform distribution is described by the probability function P[X = x_i] = 1/N, where the random variable X can take values x₁,…, x_N. A continuous uniform distribution is described by the probability density function f_X(x) = 1/(b − a) where random variable X can take values x ∈ [a,b], and by the moment generating function $M (t) = \frac{e x p (b t) - e x p (a t)}{t (b - a)}$ for $t \neq 0$ . The mean of continuous uniform distribution is (b−a)/2 and the variance is (b−a)²/12.
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