Probability density functionsAQA A-Level Further Maths: Mind map

Exam questions on Probability density 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 $P(1<X<2)$.2 marks
2. The continuous random variable $X$ has probability density function $f(x)=\frac{x}{18}$ for $0\le x\le6$, and $f(x)=0$ otherwise.
   Find the median of $X$.2 marks
3. The continuous random variable $X$ has probability density function $f(x)=kx(3-x)$ for $0\le x\le3$, and $f(x)=0$ otherwise, where $k$ is a constant.
   Show that $k=\frac29$.3 marks