Suppose that a sequence of items passes by one at a time. We want to maintain a sample of one item with the property that it is uniformly distributed over all the items that we have seen so far. Moreover we do not know the total number of items in advance and we cannot store more than one item at any time. (a) Consider the following algorithm. When the first item appears, we store it. When the k-th item appears, we replace the stored item with probability 1/k. Show that this algorithm solves the problem. (b) Now suppose that when the k-th item appears, we replace the stored item with probability 1/2. What is the distribution of the stored item in this case?

How can a user delete a drawing object

Scientists have changed the model of the atom as they have gathered new evidence. one of the atomic models is shown below. what experimental evidence led to the development of this atomic model from the one before it? a few of the positive particles aimed at a gold foil seemed to bounce back. the colors of light emitted from heated atoms had very specific energies. experiments with water vapor showed that elements combine in specific proportions. cathode rays were bent in the same way whenever a magnet was brought near them.

Why is hard disk space important to an audio engineer? why are usb ports and firewire ports useful for an audio engineer? explain in 2-3 sentences. (3.0 points) here's a list of different audio software: ableton live apple inc.'s garageband apple inc.'s logic studio digidesign's pro tools propellerhead sofware's reason sony creative software's acid pro steinberg cubase steinberg nuendo choose one of the software programs listed above, and then go to that software program's web site. read about what the software program is used for, and then write 4-5 sentences about what you learned. (10.0 points) which type of software license is the most limiting? why? explain in 2-3 sentences. (3.0 points) when sending a midi channel voice message, how can you control the volume of the sound? explain in 2-3 sentences. (4.0 points)