Insured-Assured-Be Sure

Probability Level 2

An insurance company insures a large number of homes. The insured value, X X , in ten thousands, of a randomly selected insured home, is assumed to follow a distribution with probability density function f ( x ) = 3 x − 4 , x ≥ 1. f(x) = 3x^{-4}, \text{ } \text{ } \text{ } x \geq 1. Calculate the probability that a randomly selected insured home is insured for at most 20000 20 000 .


The answer is 0.875.

Martin Soliman by Martin Soliman , 27, Philippines

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1 solution

Martin Soliman
Dec 21, 2014

We solve the given problem as follows: P [ X ≤ 20000 ] = ∫ 1 2 3 x 4 d x = − x − 3 ∣ 1 2 = − 1 8 + 1 = 7 8 = 0.875 P [X \leq 20000] = \displaystyle\int_{1}^{2} \frac{3}{x^4} \text{ } dx = \left. -x^{-3} \right|_{1}^{2} = -\frac{1}{8} + 1 = \frac{7}{8} = 0.875

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