Question

Part III. (18 Points) Show all work! No work no credit.
Let X denote the total medical expenses (in 1000s of dollars) incurred by a particular individual during a given year for a “low risk” policy. X is approximated by a continuous distribution with a pdf of:
f(x)=c(x+6)^(-5), x∈[0,∞)
Find c such that f(x) is a legitimate probability density function.

Answer 1

@DanJS

Answer 2

will my bounds for the integral be 0 to 1000?

Answer 3

@Luigi0210

Answer 4

I think I got part a figured out. I am currently on part b b) What is the expected total cost of medical expenses per individual? Find E(X). Must show all work.

Answer 5

The x E [0,inf) is my bounds for the integral?

Answer 6

@Miracrown

Answer 7

I think I got part a and part b

can you check my work for part a? Let me attach an image. give me a sec

Answer 8

sure.
the bounds 0 to \(\infty \) are correct.
you've equated the integral to 1, right?

Answer 9

yes yes I did

Answer 10

Here is my work

Answer 11

does part (b) look good?

Answer 12

I am working on part c now

Answer 13

Part (c)

Answer 14

yes,\part a,b are correct!

Answer 15

working on part d now

Answer 16

yep, part c also correct! good :)

Answer 17

don't forget to write 2000$ in part b
and not just 2.

Answer 18

thanks. I have a solution for part (d) let me attach an image.

Answer 19

How do I find part (e)?

Answer 20

oops part d is incorrect

Answer 21

k i got X_k = 2.972

Answer 22

DO I solve part e similar to part d?