Probability functions and cumulative distribution functionsEdexcel International A Level Maths: Mind map

Exam questions on Probability functions and cumulative distribution functions

1. The discrete random variable $X$ has probability function $P(X=x)=kx$ for $x=1,2,3,4$, where $k$ is a constant.
   Find $P(2\le X<4)$.2 marks
2. The discrete random variable $X$ takes the values 1, 2, 3 and 4. Its cumulative distribution function is given by $F(1)=0.15$, $F(2)=0.40$, $F(3)=0.75$ and $F(4)=1$.
   Find the probability that $X$ is either 2 or 4.2 marks
3. The discrete random variable $X$ has probability function $P(X=x)=k(x^2+1)$ for $x=0,1,2,3$, where $k$ is a constant.
   Find the value of $k$ and write down the probability function as a list of probabilities.3 marks