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Get Full Access to First Course In Probability - 8 Edition - Chapter 5 - Problem 5.2
Get Full Access to First Course In Probability - 8 Edition - Chapter 5 - Problem 5.2

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# A system consisting of one original unit plus aspare can

ISBN: 9780136033134 163

## Solution for problem 5.2 Chapter 5

First Course in Probability | 8th Edition

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Problem 5.2

A system consisting of one original unit plus aspare can function for a random amount of time X.If the density of X is given (in units of months) by what is the probability that the system functionsfor at least 5 months?

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PHYS 1010 Notes Week 12 April 4­8 General theory of relativity ­ Covers accelerating and non­accelerating reference frames ­ You can always tell if you are accelerating by dropping an object and watching it move, but we can't distinguish between an accelerating reference frame and gravity ­ Airplanes travel in curved paths because they take the shortest route possible. They fly closer to the North or South Pole and then back down because the earth is smaller further from the equator ­ Light can travel in a curved path because space itself is curved; on a curved surface, the fastest path is curved ­ So, gravity exists because mass curves space ­ Mass creates an indentation in space­time, which explains the attractive nature of gravity ­ The more massive an object is, the more it will curve space ­ Black holes ­ Forces on stars: gravity that pulls hydrogen atoms in causing fusion, which creates energy; that energy pushes everything outward (balanced with gravity) ­ Hydrogen runs out and moves on to helium and so on, which creates even more energy and the star expands outward ­ When stars start fusing iron, iron doesn't create any energy so the explosive force goes away and gravity is all that's left ­ Crushes atoms to a tiny mass, which stretches space­time a LOT ­ Nothing can escape from a black hole ­ We see black holes because we see the light going into them ­ Bending/warping space ­ Alternative to travelling at the speed of light ­ "Wormholes" describe a mass large enough to curve space ­ Newton says that light isn't affected by gravity because light doesn't have mass; Einstein says light will be affected by gravity because light curves ­ Gravitational lensing: light bending because of gravity ­ Proof of relativity The Creation of the Universe ­ The Big Bang: at the beginning of time, the universe existed at one point, which exploded, sending the universe expanding in every direction ­ Evidence: the universe is still expanding ­ The universe is 14 billion years old ­ Cosmic background radiation: noise/energy in empty space leftover from the big bang ­ Less energy where there is a lot of mass (galaxies) because energy turned into mass ­ Nothing existed before the big bang because time didn't exist until the big bang ­ Big Bang ­­> particles combine to form bigger particles in the first three minutes ­ Because light from super far stars are still traveling toward us, we can look at things really far away and be looking back in time The Death of the Universe ­ Possibilities: 1. There's not enough mass for gravity to overcome the force of the Big Bang ­­> the universe will continue to expand forever ­ The further things go, the faster they move 2. There's lots of mass and gravity will overcome the force of the Big Bang ­­> the universe will slow down and reverse, with the end in a "big crunch" 3. The force of gravity and the energy from the Big Bang are perfectly matched ­­> expansion slows down and approaches zero, and then we don't know what happens next ­ Evidence suggests the universe is close to this possibility ­ There's a lot of mass in our galaxy that we can't measure; we know it's there because otherwise our galaxy wouldn't hold together ­ "Dark matter"; does not interact with light ­ We don't know how much there is ­ The expansion of the universe is increasing/accelerating, which does not make sense because gravity should be slowing it down ­ "Dark energy" Atoms ­ Robert Brown saw that pollen grains and water were moving under a microscope ­ JJ Thompson discovered a cathode­ray tube: wireless transmission, sending light that bent near magnets (electrons) from one place to another ­ Discovery of electron ­ Millikan was able to measure the charge/mass of an electron ­ Rutherford realized atoms have a positively charged nucleus ­ Discovery of proton

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