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Science, Technology, Engineering and Mathematics
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Into the Exponential Distribution
Get into the exponential distribution through an exploration of its pdf.
The pdf $f(x)$ of an exponential distribution with parameter $\lambda$ is
$$f(x) = \lambda \exp(-\lambda x)\quad x\geq 0$$
The cdf $F(x)$ of such a distribution is
$$F(x) = \int^x_0 f(x') dx'$$
Use your analytical skills to answer these questions:
1. Must the pdfs of two different exponential distributions intersect?
2. In what cases do $F(x)$ and $f(x)$ intersect?
3. Can the cdfs for two exponential distributions intersect?
4. Can the pdfs for three different exponential distibutions intersect at the same point?
You might want to experiment with specific choices of $\lambda$ before constructing more general arguments.
Mathematical reasoning & proof
Manipulating algebraic expressions/formulae
Making and proving conjectures
Definite and indefinite integration
Probability density functions
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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