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# Normal Intersection

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Age 16 to 18

Challenge Level

- Problem

Imagine that I plot the pdfs for two normal distributions on the
same axes. Could I choose the parameters so that the curves
intersect $0$, $1$ or $2$ times?

Imagine that I plot the cdfs for two normal distributions on the same axes. Could I choose the parameters so that the curves intersect $0$, $1$ or $2$ times?

Imagine that I plotted the pdf and the cdf of normal distribution on the same axes. Would they always, sometimes or never intersect?

Give examples or convincing arguments to support your reasoning. You might want to experiment with specific choices of parameters before attempting to construct more general arguments.

Imagine that I plot the cdfs for two normal distributions on the same axes. Could I choose the parameters so that the curves intersect $0$, $1$ or $2$ times?

Imagine that I plotted the pdf and the cdf of normal distribution on the same axes. Would they always, sometimes or never intersect?

Give examples or convincing arguments to support your reasoning. You might want to experiment with specific choices of parameters before attempting to construct more general arguments.