STATS2107 - Statistical Modelling & Inference II - QUIZ
STATS2107 · Statistical Modelling & Inference II
The University of Adelaide
Questions
10 Questions
Practice 10 questions on STATS2107 - Statistical Modelling & Inference II at The University of Adelaide. Free AI-generated quiz on uNotes — track your score, retake anytime.
Define the Mean Squared Error (MSE) of an estimator T for a parameter $\theta$.
2What is the definition of bias for an estimator T of a parameter $\theta$?
3Prove the relationship between Mean Squared Error (MSE), Variance, and Bias: $MSE_T(\theta) = Var(T) + b_T(\theta)^2$.
4For i.i.d. $N(\mu, \sigma^2)$ random variables $Y_1, \ldots, Y_n$, what is the Mean Squared Error of the sample mean $\overline{Y}$ as an estimator for $\mu$?
5Define the t-distribution with $k$ degrees of freedom.
6Which of the following statements are true regarding the t-distribution?
7Consider the simple linear regression model $Y_i = \beta_0 + \beta_1 x_i + \epsilon_i$, where $\epsilon_i \sim N(0, \sigma^2)$ are independent. If $\hat{\beta}_1 = \frac{S_{xy}}{S_{xx}}$, what is $E[\hat{\beta}_1]$?
8For the simple linear regression model $Y_i = \beta_0 + \beta_1 x_i + \epsilon_i$, with $\epsilon_i \sim N(0, \sigma^2)$ i.i.d., what is the variance of the estimated slope $\hat{\beta}_1$?
9In the context of linear regression, which of the following are assumptions of the model?
10Given a sample $y_1, \ldots, y_n$ from a Poisson distribution with parameter $\lambda$, what is the maximum likelihood estimate (MLE) of $\lambda$?
