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 random variable 2−3X is of the form aX+b, with a=−3 and b=2. Thus, Var(2−3X)=(−3)2Var(X)=9⋅2=18. Is it always true that $E[X^2]≥(E[X])^2$? We know ...

Abstract: In this paper, we derive the probability mass function (PMF) and the cumulative mass function (CMF) of the sum of discrete independent and identically distributed random variables. As an ...

Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...

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, ...

Stochastic dominance (SD) theory is concerned with orderings of random variables by classes of utility functions characterized solely in terms of general properties. This paper discusses a type of ...

The DARMA (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A DARMA ...

Abstract: Inference of causal structure in random variables from observed data only is a crucial science problem. This study categorizes the causal relationship between two discrete random variables ...