random-variables

What does it mean: 'The inf is only needed when measuring the quantile of distributions that have regions with no probability'?

What does it mean: 'where R(x) denotes the possible realizations rendered from the random variable X'?

Learning objectives: Use sample data to estimate quantiles, including the median. Estimate the mean of two variables and apply the CLT. Estimate the covariance and correlation between two random variables. Explain how coskewness and cokurtosis are related to skewness and kurtosis. Questions...

Learning objectives: Define covariance and explain what it measures. Explain the relationship between the covariance and correlation of two random variables and how these are related to the independence of the two variables. Explain the effects of applying linear transformations on the...

Learning objectives: Explain the differences between a probability mass function and a probability density function. Characterize the quantile function and quantile-based estimators. Explain the effect of a linear transformation of a random variable on the mean, variance, standard deviation...

Learning objectives: Describe and distinguish a probability mass function from a cumulative distribution function and explain the relationship between these two. Understand and apply the concept of a mathematical expectation of a random variable. Describe the four common population moments...

AIM: Define, calculate, and interpret the covariance and correlation between two random variables. Questions: 304.1. Two assets, X and Y, produce only three joint outcomes: Prob[X = -3.0%, Y = -2.0%] = 30%, Prob[X = +1.0%, Y = +2.0%] = 50%, and Prob[X = +5.0%, Y = +3.0%] = 20%: What is...