Further Mathematics 7366: Statistics Topical Past Paper Questions

The continuous random variable X has probability density function $$ \mathrm{f}(x)=\left\{\begin{aligned}&\frac{3x}{44}+\frac{1}{22}&\quad1\leq x\leq5\\ &0&\quad&otherwise\end{aligned}\right. $$ (a) Find $ P(X > 2) $ [2 marks] (b) Find the upper quartile of X Give your answer to…

The continuous random variable X has probability density function $ f(x) $ It is given that $ f(x) = x^{2} $ for $ 0 \leq x \leq 1 $ It is also given that $ f(x) $ is a linear function for $ 1 Show that $ \mathrm{Var}(X) = 0.0864 $ correct to three significant figures.

Wade and Odelia are investigating whether there is an association between the region where a person lives and the brand of washing powder they use. They decide to conduct a $ \chi^{2} $-test for association and survey a random sample of 200 people. The expected frequencies for th…