4. (30 points) For each m E N, let {X," }TEN/m be a Bernoulli process in- dexed by the integer multiples of 1/m with success probability Pm. Let {Y," )TEN/m be another, independent Bernoulli process indexed by the in- teger multiples of 1/m with success probability q > 0. Define a third processs {Z" }TEN/m by Zm : Xmym for r EN/m. (a) Let Tm = inf{r EN/m|Zm =1}. What is the name of the distribu- tion of mTm including any parameters? (b) What is the limiting distribution of I'm as m -+ 0o