This video was made to answer a students question, "What is the difference between the Poisson Distribution and Exponential Distribution, and how do I know which one to use?" Great question Danielle! Hope this helps.
I just spent a lot of time thinking about why lambda is 2 in this problem. I could agree intuitively, but the explanation wasn't working with how I'd defined/understood variables. So, I'm going to share this note without rambling more about my confusion. Lambda is 2 because (20 min)*(6 problems / 60 minutes) = 2 problems in the redefined interval (and also happens to be the number asked for in the question). We redefined lambda (the number of events) according to a smaller subinterval, given what we were told about the mean of the distribution on the interval of an hour. This complies with a part of the definition of the Poisson: The probability of one count in a subinterval is the same for all subintervals and proportional to the length of the subinterval. And, this also helped me: If a Poisson random variable represents the number of counts in some interval, the mean of the random variable must equal the expected number of counts in the same length of interval.
thank you.... so basically in poisson we decide our unit as per requirement... here we took 20minutes = 1 unit.... and for exponential we keep unit as it is ?? does this make sense... did i understand or i messed up somewhere?
Great Question! Since the question concerns probability in terms of minutes, we want to have lambda in terms of minutes. In other words, we want problems per minute.
very nicely explained. thank you so much for the video! i just have a question... when we're dealing w Poission, why do we exclude the upper number when we're dealing with inequalties like P(X< 2)? why do we exclude the 2? I've seen this happen in my workbook as well and it's been confusing me. i find it strange because even in this one example I saw elsewhere, even with an inequality like P(X
