Question

An insurance company issues a policy covering losses up to 5 (in thousands of dollars). The loss, $X$ , follows a distribution with density function: $$f(x)=\left\{\begin{array}{cc}{\frac{3}{x^{4}}} & {x \geq 1} \\ {0} & {x<1}\end{array}\right.$$ What is the expected value of the amount paid under the policy?

          An insurance company issues a policy covering losses up to 5 (in thousands of dollars). The loss, $X$ , follows a distribution with density function:
$$f(x)=\left\{\begin{array}{cc}{\frac{3}{x^{4}}} & {x \geq 1} \\ {0} & {x<1}\end{array}\right.$$
What is the expected value of the amount paid under the policy?

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Added by Raquel H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ahmet Yavas

06/19/2022

Step 1

The expected value of a random variable is the sum of the product of each outcome and its probability. In this case, the expected value of the loss is the integral from 1 to infinity of x*f(x) dx. However, the policy only covers losses up to 5, so we need to Show more…

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An insurance company issues a policy covering losses up to 5 (in thousands of dollars). The loss, $X$ , follows a distribution with density function: $$f(x)=\left\{\begin{array}{cc}{\frac{3}{x^{4}}} & {x \geq 1} \\ {0} & {x<1}\end{array}\right.$$ What is the expected value of the amount paid under the policy?

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