Mean, variance, mode, median and quartilesEdexcel International A Level Further Maths: Mind map

Exam questions on Mean, variance, mode, median and quartiles

1. The continuous random variable $X$ has probability density function $f(x)=\frac{3x^2}{8}$ for $0\le x\le2$, and $f(x)=0$ otherwise.
   Find the probability that $X$ is greater than its mean.2 marks
2. The continuous random variable $Y$ has probability density function $f(y)=\frac y2$ for $0\le y\le2$, and $f(y)=0$ otherwise.
   Write down the mode of $Y$, giving a reason.2 marks
3. The continuous random variable $X$ has probability density function $f(x)=12x^2(1-x)$ for $0\le x\le1$, and $f(x)=0$ otherwise.
   Find the mode of $X$.3 marks