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Libniz Group Title

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.

  • 2 years ago
  • 2 years ago

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  1. Libniz Group Title
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    @satellite73

    • 2 years ago
  2. Libniz Group Title
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    I am having trouble setting it up

    • 2 years ago
  3. satellite73 Group Title
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    ok i have to think geometric distribution is \(P(n) = p(1-p)^n\) right?

    • 2 years ago
  4. Libniz Group Title
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    yes

    • 2 years ago
  5. satellite73 Group Title
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    jesus i have no idea. it tell you average is \(T_1\) and i think that means \(\frac{1-p_1}{p_1}=T_1\)

    • 2 years ago
  6. satellite73 Group Title
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    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 ?

    • 2 years ago
  7. Libniz Group Title
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    no, this is a practice exam

    • 2 years ago
  8. Libniz Group Title
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    that's ok, thanks for your help

    • 2 years ago
  9. satellite73 Group Title
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    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 \(p_1T_1+p_2T_2\)

    • 2 years ago
  10. satellite73 Group Title
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    no that isn't right either, at least i don't think so what text are you using?

    • 2 years ago
  11. Libniz Group Title
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    I am actually having troubling understanding what is being asked

    • 2 years ago
  12. satellite73 Group Title
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    i think you are being asked the following: pick a device at random, put \(X\) = amount of time it runs. Find the distribution of \(X\)

    • 2 years ago
  13. satellite73 Group Title
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    in other words, find a formula for \(P(X=k)\) the probability the device runs for time \(k\)

    • 2 years ago
  14. satellite73 Group Title
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    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

    • 2 years ago
  15. Libniz Group Title
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    probability and schocastic process by yates

    • 2 years ago
  16. satellite73 Group Title
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    nope, sorry

    • 2 years ago
  17. Libniz Group Title
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    @phi

    • 2 years ago
  18. phi Group Title
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    do you know how to combine two geometric distributions?

    • 2 years ago
  19. Libniz Group Title
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    no

    • 2 years ago
  20. phi Group Title
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    that is what they are asking

    • 2 years ago
  21. satellite73 Group Title
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    i should delete my embarrassing answer now we will get a real one i hope

    • 2 years ago
  22. Libniz Group Title
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    can you show me how to combine distributions

    • 2 years ago
  23. phi Group Title
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    No answer from me, I never learned this stuff. But it might be a negative binomial distribution.

    • 2 years ago
  24. Libniz Group Title
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    alright, thanks anyway

    • 2 years ago
  25. phi Group Title
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    if you get the answer, please post it.

    • 2 years ago
  26. Libniz Group Title
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    I will ask zarkon, when he comes on; hopefully before my quiz though

    • 2 years ago
  27. Libniz Group Title
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    @zarkon

    • 2 years ago
  28. Zarkon Group Title
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    is that the full problem?

    • 2 years ago
  29. Libniz Group Title
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    yes

    • 2 years ago
  30. Zarkon Group Title
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    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

    • 2 years ago
  31. Libniz Group Title
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    screen shot in case I mistyped something

    • 2 years ago
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  32. Zarkon Group Title
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    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 \[P(X\le x)=P((X\le x,d1)\text{ or }(X\le x,d2))\] \[=P(X\le x|d1)P(d1)+P(X\le x|d2)P(d2)\]

    • 2 years ago
  33. Zarkon Group Title
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    \[=P(X\le x|d1)p1+P(X\le x|d2)p2\]

    • 2 years ago
  34. Zarkon Group Title
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    though I could be misinterpreting the problem (since I don't think it is totally clear)

    • 2 years ago
  35. Libniz Group Title
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    yeah, I had hard time even understanding what they were asking for

    • 2 years ago
  36. Zarkon Group Title
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    I would ask your prof...problem isn't clear to me and I have taught courses in mathematical statistics.

    • 2 years ago
  37. Libniz Group Title
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    so this is conditional probability problem?

    • 2 years ago
  38. Zarkon Group Title
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    based on what read it looks like you need to use conditional prob for at least part of the problem

    • 2 years ago
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