# Not a "normal" question

Calculus Level 3

Sketch the probability density function of a normal distribution with some mean and standard deviation. Call this graph $$f(x)$$.

Define $$g(n)=$$ number of turning points $$f^{(n)}(x)$$ has, where $$f^{(n)}(x)$$ is the $$n^{th}$$ derivative of $$f(x)$$.

What is the value of $$\sum_{n=0}^{20} g(n)$$?

BONUS: can you generalise this for $$\sum_{n=0}^{k} g(n)$$?

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