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Given a probability density function find the mean, median and mode of the distribution.

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Circle pdf

What happens if this pdf is the arc of a circle?

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Scale Invariance

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.


Age 16 to 18 Challenge Level:

You will need to find cdf = pdf = f(x) for some f(x).

What conditions must f(x) satisfy if it to to be a pdf? What conditions must it satisfy if it is to be a cdf? Why is the condition $F(x)\neq 1$ important?

For a given random variable, how are the pdf and cdf related to each other?