The problem of estimating the variance of the ratio estimator in sampling with probability proportional to aggregate size is investigated. The form of nonnegative unbiased variance estimators is found ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

The problem of estimating the probability of an odd number of successes in n independent Bernoulli trials in minimum variance unbiased fashion is addressed. It is shown that this single problem, which ...

According to recent macroeconomic studies, microeconomic shocks can generate aggregate fluctuations (the granular hypothesis). I test this idea by studying the variance and tail probability of ...