Solution Found!
The total amount of medical claims (in $100,000) of the
Chapter 3, Problem 19E(choose chapter or problem)
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