Continuous random variables: past paper questions

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• Question 6Oct/Nov 2023, paper 61Structured8 marksHas a diagram

  A continuous random variable $X$ takes values from 0 to 6 only and has a probability distribution that is symmetrical. Two values, $a$ and $b$, of $X$ are such that $\mathrm{P}(a<X<b)=p$ and $\mathrm{P}(b<X<3)=\frac{13}{10}p$, where $p$ is a positive constant.

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• Question 3May/June 2026, paper 63Structured6 marks

  A random variable $X$ takes values between 0 and 6 only and has probability density function $\mathrm{f}(x)$ as shown in the diagram, where $a$ is a constant. Given that $\mathrm{E}(X)=2$, find $\mathrm{Var}(X)$.

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• Question 6May/June 2024, paper 61Structured8 marks

  The diagram shows the graph of the probability density function, $\mathrm{f}$, of a random variable $X$. The graph is a quarter circle entirely in the first quadrant with centre $(0,0)$ and radius $a$, where $a$ is a positive constant. Elsewhere $\mathrm{f}(x)=0$.

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• Question 2May/June 2023, paper 61Structured8 marksHas a diagram

  The graph of the function f is a straight line segment from $(0,0)$ to $(2,1)$. Show that f could be a probability density function.

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• Question 7May/June 2023, paper 62Structured8 marks

  The diagram shows the graph of the probability density function, $\mathrm{f}$, of a random variable $X$ which takes values between 0 and 4 only. Between these two values the graph is a straight line.

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• Question 7May/June 2023, paper 63Structured8 marksHas a diagram

  A random variable $X$ has probability density function $\mathrm{f}$, where the graph of $y=\mathrm{f}(x)$ is a semicircle with centre $(0,0)$ and radius $\sqrt{\frac{2}{\pi }}$, entirely above the $x$-axis. Elsewhere $\mathrm{f}(x)=0$ (see diagram).

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