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Let f x denote the probability density function of a normal

Let f(x) denote the probability density function of a normal random variable with mean μ and variance σ2. Show that μ − σ and μ + σ are points of inflection of this function. That is, show that

f″(x) = 0 when x = μ − σ or x = μ + σ.

f″(x) = 0 when x = μ − σ or x = μ + σ.

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