Probability, Where do I start??
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 T2T1.
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.

Question

Probability, Where do I start??
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.

anonymous · Answer

So, I think to find the probability P for the geometric distribution, I need to solve for E[X], which is equal to p1*E[X|T1] + p2*E[X|T2] ... and it should be equal to 1/p, so the probability p is equal to 1/(p1*E[X|T1] + p2*E[X|T2]) and I just plug that in to the geometric form equation? So I get 

 $$P_X(X) = 1/(p_1*E[X|T_1] + p_2*E[X|T_2]) * (1- 1/(p_1*E[X|T_1] + p_2*E[X|T_2]))^(x-1)$$

anonymous · Answer

This looks complex..which grade are you studying?
I had probability when I was in 12th grade..seems like I need to take a look

swag · Answer

wow

anonymous · Answer

i'm a junior in college. this is probability for engineers.

anonymous · Answer

whoa..I didn't attend college yet..I took a gap year. So, I guess I can't solve this