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

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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.

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Into the Exponential Distribution

Get into the exponential distribution through an exploration of its pdf.

Into the Normal Distribution

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

You might like to recall that the pdf of an $N(\mu, \sigma^2)$ random variable is
$$
f(x) =\frac{1}{\sqrt{2\sigma ^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}
$$
and that the probability of a value falling between $a$ and $b$ is
$$
P(a< x< b) = \int^b_a f(y)dy
$$
Don't forget that the integral is the area under the curve between two points.

Don't forget that you can look up the cumulative probabilities for a normal distribution using tables.