On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. The probability density function for the length of time it takes a runner to ...

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, ...

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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

What does the protein content in cows' milk have in common with human IQ? Both variables have approximately normal distributions. The normal distribution is a good model for measurements of many kinds ...

Abstract: This letter considers the distribution of product for two correlated real Gaussian random variables with nonzero means and arbitrary variances, which arises widely in radar and communication ...

Abstract: The law of large numbers in probability theory states that the average of random variables converges to its expected value in some sense under some conditions. Sometimes, random factors and ...

Test of independence is a fundamental problem in statistics, with many existing work including the maximal information coefficient (MIC) [1], the copula based measures [2,3], the kernel based ...