## 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. one year ago one year ago

1. Libniz Group Title

@satellite73

2. Libniz Group Title

I am having trouble setting it up

3. satellite73 Group Title

ok i have to think geometric distribution is $$P(n) = p(1-p)^n$$ right?

4. Libniz Group Title

yes

5. satellite73 Group Title

jesus i have no idea. it tell you average is $$T_1$$ and i think that means $$\frac{1-p_1}{p_1}=T_1$$

6. satellite73 Group Title

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 ?

7. Libniz Group Title

no, this is a practice exam

8. Libniz Group Title

that's ok, thanks for your help

9. satellite73 Group Title

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 $$p_1T_1+p_2T_2$$

10. satellite73 Group Title

no that isn't right either, at least i don't think so what text are you using?

11. Libniz Group Title

I am actually having troubling understanding what is being asked

12. satellite73 Group Title

i think you are being asked the following: pick a device at random, put $$X$$ = amount of time it runs. Find the distribution of $$X$$

13. satellite73 Group Title

in other words, find a formula for $$P(X=k)$$ the probability the device runs for time $$k$$

14. satellite73 Group Title

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

15. Libniz Group Title

probability and schocastic process by yates

16. satellite73 Group Title

nope, sorry

17. Libniz Group Title

@phi

18. phi Group Title

do you know how to combine two geometric distributions?

19. Libniz Group Title

no

20. phi Group Title

that is what they are asking

21. satellite73 Group Title

i should delete my embarrassing answer now we will get a real one i hope

22. Libniz Group Title

can you show me how to combine distributions

23. phi Group Title

No answer from me, I never learned this stuff. But it might be a negative binomial distribution.

24. Libniz Group Title

alright, thanks anyway

25. phi Group Title

26. Libniz Group Title

I will ask zarkon, when he comes on; hopefully before my quiz though

27. Libniz Group Title

@zarkon

28. Zarkon Group Title

is that the full problem?

29. Libniz Group Title

yes

30. Zarkon Group Title

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

31. Libniz Group Title

screen shot in case I mistyped something

32. Zarkon Group Title

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 $P(X\le x)=P((X\le x,d1)\text{ or }(X\le x,d2))$ $=P(X\le x|d1)P(d1)+P(X\le x|d2)P(d2)$

33. Zarkon Group Title

$=P(X\le x|d1)p1+P(X\le x|d2)p2$

34. Zarkon Group Title

though I could be misinterpreting the problem (since I don't think it is totally clear)

35. Libniz Group Title

yeah, I had hard time even understanding what they were asking for

36. Zarkon Group Title

I would ask your prof...problem isn't clear to me and I have taught courses in mathematical statistics.

37. Libniz Group Title

so this is conditional probability problem?

38. Zarkon Group Title

based on what read it looks like you need to use conditional prob for at least part of the problem