Statistics
Mathematical Statistics I
Train on Mathematical Statistics I with 303 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
Training
Start training
Course and path
Available problems completed
View progressLoading course progress…
Preview a course problem
See a problem from Mathematical Statistics I before you begin.
Course topics
Course topics
Parametric models and sampling distributions
Sufficiency, completeness, and exponential families
Bias, risk, consistency, and point estimation
Likelihood, score, and Fisher information
Pivots and confidence sets
Loss, risk, and introductory decision theory
Practice problems
Try a few Mathematical Statistics I problems, each with a hint.
- A parametric model is a collection of probability laws indexed by a parameter Free with an accountParametric models and sampling distributions
- For a family of densities or mass functions with respect to one fixed dominating… Sufficiency, completeness, and exponential families
- An iid Bernoulli sample of size n ≥ 1 contains K successes Likelihood, score, and Fisher information
- A hidden state θ is either zero or one Loss, risk, and introductory decision theory
- A Cauchy mean is another Cauchy, so the average does not settle Free with an accountParametric models and sampling distributions
- A complete exponential sum yields the survival UMVUE Sufficiency, completeness, and exponential families
- The unbiased sample variance is not the MSE winner Bias, risk, consistency, and point estimation
- Invariance moves the MLE but not the UMVUE Bias, risk, consistency, and point estimation
- Bernoulli information identities hold, then the bound can vanish Likelihood, score, and Fisher information
- A known-scale normal mean has a nonrandom interval length Pivots and confidence sets