A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Colorblindness is caused by a recessive gene on the X chromosome. Since men have only one X chromosome, if a man carries the colorblindness allele (gene form), he will have the trait. Women have two X ...

The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), Vol. 34, No. 1 (Mar., 1972), pp. 9-16 (8 pages) An exponential bound is obtained for probabilities of large deviations in a strictly ...

The joint probability density function \(f\) of two random variables \(X\) and \(Y\) satisfies, for every \(a_1 b_1\) and \(a_2 b_2\), \[ P(a_1\le X\le b_1, a_2\le Y ...

Stein's method has emerged as a critical framework in the study of distributional approximations, providing quantitative bounds between probability distributions through the formulation and solution ...