Distributions and expectation of DRVsAQA A-Level Further Maths: Mind map

Exam questions on Distributions and expectation of DRVs

1. The discrete random variable $X$ has probability distribution $P(X=x)=kx$ for $x=1,2,3,4$, and $P(X=x)=0$ otherwise, where $k$ is a constant.
   Find $E(X)$.2 marks
2. The discrete random variable $X$ has $P(X=1)=0.1$, $P(X=2)=0.3$, $P(X=3)=0.4$ and $P(X=4)=0.2$.
   State the mode of $X$ and find the median of $X$.2 marks
3. The discrete random variable $X$ takes the values $1,2,3,4$ with $P(X=1)=0.2$, $P(X=2)=p$, $P(X=3)=q$ and $P(X=4)=0.3$, where $p$ and $q$ are constants. It is given that $E(X)=2.6$.
   Find the values of $p$ and $q$.3 marks