Mean and variance of continuous random variablesEdexcel A-Level Further Maths: Mind map

Exam questions on Mean and variance of continuous random variables

1. The continuous random variable $X$ has probability density function $f(x)=\frac{3}{8}x^2$ for $0\le x\le 2$, and $f(x)=0$ otherwise.
   Find $\mathrm{E}\!\left(\frac{1}{X}\right)$.2 marks
2. The continuous random variable $Y$ has probability density function $f(y)=\frac{y}{2}$ for $0\le y\le 2$, and $f(y)=0$ otherwise.
   Calculate $\mathrm{E}(Y)$. Using this value, together with the mode and median of $Y$, describe the skewness of the distribution, justifying your answer.2 marks
3. The continuous random variable $X$ has probability density function $f(x)=\frac{3}{x^4}$ for $x\ge 1$, and $f(x)=0$ otherwise.
   Find the 90th percentile of $X$.3 marks