MY-ASSIGNMENTEXPERT™可以为您提供sydney STAT2011 Probability Theory概率论课程的代写代考和辅导服务！
这是悉尼大学概率论课程的代写成功案例。
STAT2011课程简介
This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. By doing this unit you will develop your statistical modelling skills and it will prepare you to learn more complicated statistical models.
Prerequisites
At the completion of this unit, you should be able to:
- LO1. construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models such as probabilities, expectations and variances
- LO2. fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters
- LO3. compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates
- LO4. assess the goodness of fit (as appropriate) of a fitted model
- LO5. apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory
- LO6. prove certain mathematical results (e.g. inequalities, limiting results) used in the course.
STAT2011 Probability Theory HELP（EXAM HELP， ONLINE TUTOR）
Find a sequence of probability measures which has both (a) subsequences which converge vaguely to a probability measure and (b) subsequences which converge vaguely to a subprobability measure which is not a probability measure.
Does there exist a sequence of subprobability measures, each which has total mass at most $1 / 2$ which converges vaguely to a probability measure?
(a). Is the collection of probability measures on the real line compact under vague convergence?
(b). Is the collection of probability measures on the real line which vanish on $(-\infty,-2) \cup(2, \infty)$ compact under vague convergence?
(c). Is the collection of probability measures on the real line which vanish on $(-\infty,-2] \cup[2, \infty)$ compact under vague convergence?
(Optional challenge problem.)
Find a sequence of random variables $\left{X_n\right}$ such that for every subsequence, one cannot normalize it and obtain a nontrivial limit. More precisely, find a sequence of random variables $\left{X_n\right}$ such that if we take any subsequence $\left{X_{n_k}\right}$, if we have sequences $a_k$ and $b_k$ with $a_k>0$ for all $k$ and such that $a_k X_{n_k}+b_k$ converges in distribution to some random variable $U$, then $U$ has a degenerate distribution.
You are not allowed to do trivial things. For example, if the $\left{X_n\right}$ ‘s are degenerate, this would be true. Or if $\left{X_n\right}$ had a point mass whose weight approached 1. To keep things nontrivial, let’s say that no $\left{X_n\right}$ can have a point mass of weight larger than $1 / 2$. I think (hope?) this will eliminate all “trivial” examples.
MY-ASSIGNMENTEXPERT™可以为您提供sydney STAT2011 Probability Theory概率论课程的代写代考和辅导服务！
