Expectation and variance of discrete random variablesEdexcel International A Level Maths: Mind map

Exam questions on Expectation and variance of discrete random variables

1. The discrete random variable $X$ has probability distribution $P(X=0)=0.2$, $P(X=1)=0.3$, $P(X=2)=0.4$ and $P(X=3)=0.1$.
   Find $E(3X+2)$.2 marks
2. The random variable $W$ has $E(W)=10$ and $\mathrm{Var}(W)=6$. The random variable $V$ is defined by $V=3W-4$.
   Find $E(W^2)$.2 marks
3. The discrete random variable $X$ takes the values 1, 2, 3 and 4 with $P(X=1)=0.1$, $P(X=2)=a$, $P(X=3)=0.4$ and $P(X=4)=b$, where $a$ and $b$ are constants. It is given that $E(X)=2.9$.
   Find the values of $a$ and $b$.3 marks