Jul20 awarded Yearling Nov26 comment Simple Renewal Process Question Only a bit. As I gathered, the distribution of the total lifetime of the component $C_t$ can be thought of as the sum of the distributions of the current age $A_t$ and the residual life $B_t$, but I don't know much of anything else regarding this matter. I should add that I'm going to bed now (I've got class in 4 hours) so if you have a formal answer to my question, I'd appreciate it if you posted it and I can ask questions about it tomorrow if I have any. Thanks for your time! Nov26 comment Simple Renewal Process Question Yes, I have seen that in class but only briefly. How can I apply that to this problem? Nov26 comment Simple Renewal Process Question Ah, you do make a good point. In that case, I'm thinking that the distribution of $A+B$ would be uniform with $E(A+B)=150$. Am I right in thinking that? Nov26 asked Simple Renewal Process Question Nov12 revised How can I make this equation flat out after 1? Formatting fix Nov12 suggested suggested edit on How can I make this equation flat out after 1? Nov12 accepted Optional Sampling Theorem Application on a Martingale Nov12 comment Optional Sampling Theorem Application on a Martingale Thanks for your response. I actually made a typo in my original post. $M_n = [(1-p)/p]^{S_n}$, not $[(1-p)p]^{S_n}$. This, however, shouldn't change your answer (aside from changing your $p(1-p)$ terms to $(1-p)/p$). Either way, this makes perfect sense. Thank you! Nov12 revised Optional Sampling Theorem Application on a Martingale added 1 characters in body Nov12 asked Optional Sampling Theorem Application on a Martingale Nov5 comment Conditional Expectation Die Roll Thanks. Is there any way to arrive at $y/2$ given the work I have in my original post? Nov5 comment Conditional Expectation Die Roll Doh, why didn't I think of that? Thanks! Nov5 accepted Conditional Expectation Die Roll Nov4 revised Conditional Expectation Die Roll added 106 characters in body Nov4 comment Conditional Expectation Die Roll Sorry for not being clear enough. What @MichaelHardy said is correct. I need to find the expected value of the first roll given the sum of the two dice. Nov4 asked Conditional Expectation Die Roll Oct28 awarded Tumbleweed Oct25 asked Optimal Stopping Example Oct10 accepted Poisson Process Arrival Probability