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.

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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 \[P_X(X) = 1/(p_1*E[X|T_1] + p_2*E[X|T_2]) * (1- 1/(p_1*E[X|T_1] + p_2*E[X|T_2]))^(x-1)\]

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

wow

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