Mean and variance of a CRVAQA A-Level Further Maths: Mind map

Exam questions on Mean and variance of a CRV

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 $\text{Var}(X)$.2 marks
2. The random variable $X$ has mean $E(X)=5$ and variance $\text{Var}(X)=4$.
   The random variable $Y=2-3X$. Find $E(Y)$ and $\text{Var}(Y)$.2 marks
3. The continuous random variable $X$ has probability density function $f(x)=\frac{2}{x^2}$ for $1\le x\le2$, and $f(x)=0$ otherwise.
   Find $E(X)$.3 marks