Question: Let X be a random variable with distribution function F. The real number m that satisfies F(m) 0.5 F(m) is called the median

Let X be a random variable with distribution function F. The real number m that satisfies F(m−) ≤ 0.5 ≤ F(m)

is called the median of this distribution function. Assuming that F is known, and that it is continuous for any real t, explain how m can be found from F.

Application: The rate of increase for the price of oil (per gallon) is described by a random variable X with distribution function

Find the median of this distribution and interpret its value. The distribution F(t) is called the logistic distribution.

F(t)= -

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