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 ...

"### If we have random variables $X_{1}+X_{1}$, $X_{2}$, $X_{3}$,..., from an independent trials process and let $S_{n} = X_{1}+X_{2}+...+X_{n}$ then we know that $S ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...

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 ...

A discrete random variable is a type of random variable that can only take on a countable number of distinct values. A discrete random variable is a variable whose possible values are distinct and ...

Example 1: A coin is flipped. Random variable X takes the value 1 if the coin lands heads, and X takes the value 0 if the coin shows tails. Example 2: Three balls are drawn without replacement from a ...

In [1], the author proposed a "rank sum" criterion for testing whether or not a sample was drawn from a population having a completely specified continuous distribution. This criterion under the null ...