Help with this little exercise

[EcoEco]

Hello,

could you help me to solve this? Thanks a lot


What is the expected value and standard deviation of T?

T=a·b·ΔT
a=10+0.1ΔT (ppm/ºC)
b=N(6,0.2) m
ΔT=N(15,4) ºC

 

[Deleted member 4993]

Hello,

could you help me to solve this? Thanks a lot


What is the expected value and standard deviation of T?

T=a·b·ΔT
a=10+0.1ΔT (ppm/ºC)
b=N(6,0.2) m
ΔT=N(15,4) ºC

What are the definitions of "expected value" and "standard deviation"?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[EcoEco]

Yes, I tried it, but I think my numbers are incorrect.

I know that if x & y are independent:
E(xy)=E(x)·E(y)
σxy^2= μx^2·σy^2 + μy^2·σx^2 + σx^2·σy^2

I did:
Total mean = (10+0.1·15)·10^-6 · 6 · 15
but I think it is incorrect

Total standard deviation I think is highly complex, due to there are three variables, and one seems depending on one of the last two variables

Any comment? Thanks a lot