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

Exam questions on Probability density and cumulative distribution functions

1. The continuous random variable $X$ has probability density function $f(x)=kx^2$ for $0\le x\le3$, and $f(x)=0$ otherwise, where $k$ is a constant.
   Find the cumulative distribution function $F(x)$ for $0\le x\le3$.2 marks
2. The continuous random variable $Y$ has cumulative distribution function $F(y)=0$ for $y<1$, $F(y)=\frac{y^2-1}{8}$ for $1\le y\le3$, and $F(y)=1$ for $y>3$.
   Find $P(1.5<Y\le2.5)$.2 marks
3. The continuous random variable $X$ has probability density function $f(x)=kx$ for $0\le x\le2$, $f(x)=k(6-2x)$ for $2<x\le3$, and $f(x)=0$ otherwise, where $k$ is a constant.
   Show that $k=\frac13$.3 marks