- #1
SpiffWilkie
- 6
- 0
You know how sometimes, you take a long time to write a question, and then you submit, but it takes you to a login screen and then you lose everything you wrote?
Anyhow...I would just like to verify some work here.
The problems states that there are 3 mutually independent random variables, X1, X2, X3, each with the pdf f(x) = 2x, 0 < x < 1.
a) What is the joint pdf?
For this, I'm assuming I just need to take the product of the three pdfs, giving me 8x1x2x3?
b) Find the expected value of 5X1X2X3.
Am I to assume that this is equal to 5 * E(X1) * E(X2) * E(X3)? If that is true, I would calculate 5 * (∫2x2dx)3 from 0 to 1?
This gives the result 40/27 ≈ 1.48
c) Find P(X1 < 1/2, X2 < 1/2, X3 < 1/2)
I calculated (∫2xdx)3 from 0 to 1/2, giving me 1/64 or .015625I'm struggling trying to connect examples from class/book/internet with actual problems given, so any help is much appreciated.
Thanks,
Steve
Anyhow...I would just like to verify some work here.
The problems states that there are 3 mutually independent random variables, X1, X2, X3, each with the pdf f(x) = 2x, 0 < x < 1.
a) What is the joint pdf?
For this, I'm assuming I just need to take the product of the three pdfs, giving me 8x1x2x3?
b) Find the expected value of 5X1X2X3.
Am I to assume that this is equal to 5 * E(X1) * E(X2) * E(X3)? If that is true, I would calculate 5 * (∫2x2dx)3 from 0 to 1?
This gives the result 40/27 ≈ 1.48
c) Find P(X1 < 1/2, X2 < 1/2, X3 < 1/2)
I calculated (∫2xdx)3 from 0 to 1/2, giving me 1/64 or .015625I'm struggling trying to connect examples from class/book/internet with actual problems given, so any help is much appreciated.
Thanks,
Steve
Last edited: