Linear functions of a DRVAQA A-Level Further Maths: Mind map

Exam questions on Linear functions of a DRV

1. The discrete random variable $X$ has $E(X)=5$ and $\mathrm{Var}(X)=4$. The random variable $Y$ is defined by $Y=3X+2$.
   Find the standard deviation of $2-4X$.2 marks
2. The number of special meals, $X$, sold at a café in one day has $E(X)=8.5$ and $\mathrm{Var}(X)=2.25$. The daily profit, in pounds, is $T=6X-20$.
   The café changes its pricing so that the daily profit becomes $T=8X-30$. Find $E(T)$ and $\mathrm{Var}(T)$.2 marks
3. The noon temperature $C$ ($^\circ$C) in a greenhouse is modelled as a discrete random variable with $E(C)=22$ and standard deviation $3$. The temperature in degrees Fahrenheit is $F=1.8C+32$.
   Find $E(F)$ and $\mathrm{Var}(F)$.3 marks