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

Scale Invariance

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

Into the Exponential Distribution

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

Into the Normal Distribution

Age 16 to 18
Challenge Level

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.