The total amount of medical claims (in $100,000) of the

Chapter 3, Problem 19E

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QUESTION:

Problem 19E

The total amount of medical claims (in $100,000) of the employees of a company has the pdf that is given by f (x) = 30x(1 − x)4, 0 < x < 1. Find

(a) The mean and the standard deviation of the total in dollars.

(b) The probability that the total exceeds $20,000.

Questions & Answers

QUESTION:

Problem 19E

The total amount of medical claims (in $100,000) of the employees of a company has the pdf that is given by f (x) = 30x(1 − x)4, 0 < x < 1. Find

(a) The mean and the standard deviation of the total in dollars.

(b) The probability that the total exceeds $20,000.

ANSWER:

Answer

Step 1 of 5

The pdf is  f (x) = 30x(1 − x)4, 0 < x < 1

a)E(x)=x f(x) dx

         =30x2(1-x)4 dx

        =30x2(1-4x+6x2-4x3 +x4) dx

        =30x2-4x3+6x4-4x5+x6) dx

        =30

        =2/7=0.2857


       

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