1. Suppose that the error in the reaction temperature, in ◦C, for a controlled laboratory experiment is a continuous random variable X having the probability density function
f(x)=x2/3 for −1 <x<2,
f(x)=0, elsewhere
(a) Verify that f(x) is a density function
(b) Find P(0 <X≤ 1).
1
Expert's answer
2020-04-27T16:41:49-0400
"a)\\int_{-\\infty}^{\\infty}f(x)dx=1\\\\\n\\int_{-1}^{2}\\frac{2}{3}xdx=[\\frac{2}{3}\\frac{x^2}{2}]_{-1}^2=1.\\text{ So } f(x)\\text{ is pdf}."
Dear Kat, thank you for leaving a feedback. We found that cases 2x/3
and 1/3*x^2 meet conditions of the question. In other words, expert's
solution is not wrong.
Kat
24.02.21, 23:42
I think for part b of this problem, they meant to say (x²)/3, in
which case the answer to b is 1/9. Because the integral from 0 to 1 of
(x²)/3 is (x³)/9 from 0 to 1 which equals 1/9. At least that's how
my stats professor solved this problem. Just in case someone came here
for that!
Leave a comment
Thank you! Your comments have been successfully added. However, they need to be checked by the moderator before being published.
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
Finding a professional expert in "partial differential equations" in the advanced level is difficult.
You can find this expert in "Assignmentexpert.com" with confidence.
Exceptional experts! I appreciate your help. God bless you!
Comments
Dear Kat, thank you for leaving a feedback. We found that cases 2x/3 and 1/3*x^2 meet conditions of the question. In other words, expert's solution is not wrong.
I think for part b of this problem, they meant to say (x²)/3, in which case the answer to b is 1/9. Because the integral from 0 to 1 of (x²)/3 is (x³)/9 from 0 to 1 which equals 1/9. At least that's how my stats professor solved this problem. Just in case someone came here for that!
Leave a comment