Two grocers agree that the daily demand for a particular item has Poisson distribution. However, grocer $A$ claims that the mean demand is $3$ items per day, while grocer $B$ claims that the mean demand is $6$ items per day.   They agree to resolve the disagreement by observing the demand on one particular day: $B$ agrees to accept $A$’s claim if the observed demand is $4$ or less, and $A$ agrees to accept $B$’s claim if the observed demand is $5$ or more.  (a) Calculate the probability that $A$’s claim is accepted when, in fact, $B$’s claim is correct
I want to find the probability that mean is less than 5 given that poisson distribution states it is 6 ie find p(x&lt;5|x~po(6))  Here is the actual question: Two grocers agree that the daily demand for a particular item has Poisson distribution. However, grocer A claims that the mean demand is 3 items per day, while grocer B claims that the mean demand is 6 items per day. They agree to resolve the disagreement by observing the demand on one particular day: B agrees to accept A’s claim if the observed demand is 4 or less, and A agrees to accept B’s claim if the observed demand is 5 or more. (a) Calculate the probability that A’s claim is accepted when, in fact, B’s claim is correct
Looking to achieve frame effect with shadows at corners Replicate the Fourier transform time-frequency domains correspondence illustration using TikZ Skype doesn't work in Ubuntu 14.04 Checking if array is multidimensional or not? What is the most efficient way to check if an array is a flat array of primitive values or if it is a multidimensional array? Is there any way to do this without actually looping through an array and running is_array() on each of its elements? Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$ If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light? I know that as the velocity increases, the mass of the object also increases so it becomes tougher and tougher to move the object which ultimately leads to a requirement of infinite energy to accelerate an object to the speed of light. But I have a doubt.  As far as I know only the observable mass (Relativistic mass) increases but not the Proper Mass or Intrinsic Mass, right? The actual mass of the object will remain the same. So if the actual mass ($m_0)$ remains the same and only the observable mass increases, why is more and more energy required? I know that even if the object exceeds the speed of light, we will not be able to say that it is moving faster than the speed of light but is it possible to make it move faster than light?  If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?  I quote Igor Ivanov (a stackexchange user from this question ) to give an insight into my question.     The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to  popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".   EDIT  After reading the answers I have a doubt.  SO can I say that only the overall energy of the system increases while the mass remains constant? But then if mass remains constant, then why is more and more energy gradually required? I mean there should be a reason for that requirement of infinite energy. How to record how much time user has spent on my node? I want to record the time a user has spent on my particular node so I could show a pop up to the user to register once the user has read 3 article. But the user must have spent at least 30 seconds on each node.   There is the  module available, but I wonder if I can merge it with another (custom) module I have created (which records the number of nodes user have visited)? What's the best way of accessing field in the enclosing class from the nested class? Why does a balloon spiral in the air instead of moving in a straight line? Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves? Can you be sued for using publicly used images on a blog without copyright permission? What is the difference between "accumulative" and "cumulative"? I'm having a hard time understanding the real distinction between  and .  accumulative     adjective         tending to accumulate or arising from accumulation; cumulative.   tending to accumulate wealth; acquisitive.      cumulative     adjective         increasing or growing by accumulation or successive additions: the cumulative effect of one rejection after another.   formed by or resulting from accumulation or the addition of successive parts or elements.   of or pertaining to interest or dividends that, if not paid when due, become a prior claim for payment in the future: cumulative preferred stocks.      These definitions (and those from other dictionaries as well) say different things but I can't understand how they aren't really meaning the same thing.  Yet, when thinking about it, it seems there are some cases where it is distinctly more correct to use one or the other.  What's the difference, practically? Copy files from Network Mapped Drive I am trying to copy a file over from a mapped drive on a network to the current computer through a batch file.   I've already attempted the following below and still no results. The plan is to run a batch file to copy a file from a network drive down to the local C:\ drive.   @echo off copy H:\Videos\TargetVideo\TargetVideo.mp4 C:\Video\ I want to know all sets of single-variate functions that fulfill the following qualities: $\forall_{f:R^2 \to R^2} \forall_{g \in CAF} \forall_{h \in CAF} \exists_{k\in CAF} k(x) = f(g(x),h(x))$ where CAF is the set I am wishing to find. I know that the set of constants and the set of piece wise constants each satisfy that equation. Do any others? Why did Douglas Adams pick 42 as the ultimate answer? Star Trek often refers to 47 and Star Trek made a sport out of finding real or imagined references to 47. Why did Douglas Adams pick 42 as the ultimate answer in the Hitchhikers guide to the galaxy? Abstraction VS Information Hiding VS Encapsulation Can you tell me what is the difference between abstraction and information hiding in software development?  I am confused. Abstraction hides detail implementation and information hiding abstracts whole details of something.  Update: I found a good answer for these three concepts.  for several citations taken from . How did they post process before Photoshop? Sending Email in Android using JavaMail API without using the default/built-in app I have come across both the phrases - 'on the internet' and 'over the internet.'   I'm pretty sure that both are correct but then which to use when?  Please note, I'm well aware of all over the Internet which I'm not concerned about. "The operation couldn’t be completed. (BKAgentServiceErrorDomain error 8.)"