Mathematics S1,S2,S3 WST01: Estimation, Confidence Intervals, and Tests Topical Past Paper Questions

The random variable X has a continuous uniform distribution over the interval $ [a-1, a+5] $ where a is a constant. The mean of a random sample of size 9, taken from this distribution, is denoted by $ \bar{X} $ (a) Find, in terms of $\bar{X}$, an unbiased estimator for $a$ (3) (b…

A population has an unknown mean $ \mu $ and an unknown variance $ \sigma^{2} $ A random sample represented by $ X_{1}, X_{2}, \ldots, X_{20} $ is taken from the population. (a) Explain why $ \frac{1}{2}X_{1}+\frac{3}{4}X_{20} $ is a statistic. (1) (b) Show that $ R = \frac{1}{2}…

The continuous random variable D is uniformly distributed over the interval $ [x - 1, x + 5] $ where x is a constant. A random sample of $n$ observations of $D$ is taken, where $n$ is large. (a) Use the Central Limit Theorem to find an approximate distribution for $\overline{D}$…