Question: 8. Let X be a random variable with distribution function F. For p (0 < p < 1), Qp is said to be a quantile

8. Let X be a random variable with distribution function F. For p (0 < p < 1), Qp is said to be a quantile of order p if F (Qp−) ≤ p ≤ F (Qp). In a certain country, the rate at which the price of oil per gallon changes from one year to another has the following distribution function: F (x) = 1 1 + e−x , −∞ < x < ∞. Find Q0.50, called the median of F; Q0.25, called the first quartile of F; and Q0.75, called the third quartile of F. Interpret these quantities.

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