Mean and variance of discrete distributionsEdexcel A-Level Further Maths: Mind map

Exam questions on Mean and variance of discrete distributions

1. The discrete random variable $X$ has $P(X=1)=0.1$, $P(X=2)=0.3$, $P(X=3)=0.4$ and $P(X=4)=0.2$.
   Find $E\left(\frac1X\right)$.2 marks
2. The discrete random variable $Y$ has probability function $P(Y=y)=ky$ for $y=1,2,3,4,5$, where $k$ is a constant.
   Find $\text{Var}(Y)$.2 marks
3. A fairground game costs £3 to play. A player is paid £20 with probability $0.05$, £6 with probability $0.2$ and nothing otherwise. Let $X$ be the player's profit in pounds, where profit is the payout minus the £3 cost.
   Find $E(X)$ and interpret your answer in context.3 marks