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 first step is to ensure that the given distribution actually is a valid probability distribution. As mentioned earlier, ...

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 ...

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: This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions ...

Given N ten sided dice, and a target number k, what is the probability of acheiving at least n successes if:<BR><BR>a) A die is counted a success if the number rolled on it is greater to or equal to ...

Density functions are nonnegative for all real numbers but greater than zero only at a finite or countably infinite number of points. Density functions are nonnegative for all real numbers and are ...