anonymous
  • anonymous
A production line yields two types of devices: Type1 devices occur with probability p1 and work for an average time T1, Type2 devices occur with probability p2 and work for an average time T2, such that p1+p2=1 and T2>T1. The time a device works is modeled as a geometrical distribution. Let X be the time a device chosen uniformly at random works. Find the distribution of X.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
I am having trouble setting it up
anonymous
  • anonymous
ok i have to think geometric distribution is \(P(n) = p(1-p)^n\) right?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes
anonymous
  • anonymous
jesus i have no idea. it tell you average is \(T_1\) and i think that means \(\frac{1-p_1}{p_1}=T_1\)
anonymous
  • anonymous
let me try to write this correctly \[T_1=\frac{p_2}{p_1}\] and \[T_2=\frac{p_1}{p_2}\] but i am not sure that helps solve the problem do you have an example to work off of ?
anonymous
  • anonymous
no, this is a practice exam
anonymous
  • anonymous
that's ok, thanks for your help
anonymous
  • anonymous
ok forget that last noise i wrote, it is ridiculous and i am embarrassed maybe it is much simpler we pick device \(T_1\) with probability \(p_1\) and device \(T_2\) with probability \(p_2\) could it be as simple as \(p_1T_1+p_2T_2\)
anonymous
  • anonymous
no that isn't right either, at least i don't think so what text are you using?
anonymous
  • anonymous
I am actually having troubling understanding what is being asked
anonymous
  • anonymous
i think you are being asked the following: pick a device at random, put \(X\) = amount of time it runs. Find the distribution of \(X\)
anonymous
  • anonymous
in other words, find a formula for \(P(X=k)\) the probability the device runs for time \(k\)
anonymous
  • anonymous
but really i am stuck so i should shut up. but perhaps i have a text with something similar, which is why i asked what text you were using
anonymous
  • anonymous
probability and schocastic process by yates
anonymous
  • anonymous
nope, sorry
anonymous
  • anonymous
@phi
phi
  • phi
do you know how to combine two geometric distributions?
anonymous
  • anonymous
no
phi
  • phi
that is what they are asking
anonymous
  • anonymous
i should delete my embarrassing answer now we will get a real one i hope
anonymous
  • anonymous
can you show me how to combine distributions
phi
  • phi
No answer from me, I never learned this stuff. But it might be a negative binomial distribution.
anonymous
  • anonymous
alright, thanks anyway
phi
  • phi
if you get the answer, please post it.
anonymous
  • anonymous
I will ask zarkon, when he comes on; hopefully before my quiz though
anonymous
  • anonymous
@zarkon
Zarkon
  • Zarkon
is that the full problem?
anonymous
  • anonymous
yes
Zarkon
  • Zarkon
I'm a little confused ... Type1 devices occur with probability p1 ... Type2 devices occur with probability p2 vs "a device chosen uniformly" are they chosen uniformly or with probabilities p1,p2
anonymous
  • anonymous
screen shot in case I mistyped something
1 Attachment
Zarkon
  • Zarkon
I don't think the problem is worded very well especally near the end. here is how I see the problem let \(d1,d2\) be device 1 and device 2 then \[P(X\le x)=P((X\le x,d1)\text{ or }(X\le x,d2))\] \[=P(X\le x|d1)P(d1)+P(X\le x|d2)P(d2)\]
Zarkon
  • Zarkon
\[=P(X\le x|d1)p1+P(X\le x|d2)p2\]
Zarkon
  • Zarkon
though I could be misinterpreting the problem (since I don't think it is totally clear)
anonymous
  • anonymous
yeah, I had hard time even understanding what they were asking for
Zarkon
  • Zarkon
I would ask your prof...problem isn't clear to me and I have taught courses in mathematical statistics.
anonymous
  • anonymous
so this is conditional probability problem?
Zarkon
  • Zarkon
based on what read it looks like you need to use conditional prob for at least part of the problem

Looking for something else?

Not the answer you are looking for? Search for more explanations.