You use replica plating to isolate a culture of an E. coli a…

You use replica plating to isolate a culture of an E. coli auxotroph, unable to grow without tryptophan, from a culture of prototrophs. For a number of months, you propagate your tryptophan auxotroph culture on GSA (glucose salts agar) medium supplemented with tryptophan. One day, you mistakenly transfer some of your strain onto a new GSA plate that does not contain tryptophan. You realize your mistake after you have left the lab for the day and it is too late to correct it. However, when you return following 24 hours of incubation, you discover a few colonies of E. coli growing on the GSA medium. Please explain this result: why were you able to originally obtain a tryptophan auxotroph from a prototroph culture, and why months later did you find E. coli growth on GSA lacking tryptophan?

Consider the experiment of taking this exam. Suppose we mode…

Consider the experiment of taking this exam. Suppose we model your score for this exam as Y=5X, where X is a discrete uniform random variable over {0,1,…,N}, and N is the total number of questions. Note that X represents a random variable which is the total number of questions you get right. Find