Question 1069288
Start with a tree diagram
X ========p(x)=============X*p(x)
10^-2======5/12=15/36=======.004167; I get 10^-2 from 10^-4*10^2, probabilities 1/2 and 5/6
10^-1======5/18=10/36=======.027778; probabilities 1/3 and 5/6
1=========8/36============.222222; two-5/6*1/6 and 1/6 and 1/2
10========1/18=2/36========.555556
100=======1/36============2.777778
E(X)=3.5875 seconds.