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Let A1, A2, A3, ... be a sequence of events of a sample

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani ISBN: 9780131453401 223

Solution for problem 28 Chapter 1.4

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Problem 28

Let A1, A2, A3, ... be a sequence of events of a sample space. Prove that P *+ n=1 An , . n=1 P (An). This is called Booles inequality.

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Geology 101 Notes April 7 th Energy and Mineral Resources ­ Sources of energy ­ Oil and natural gas formation and extraction ­ Coal formation energy sources ­ Ores and minerals Where does energy come from ­ Sun o Solar energy o Plant matter o Fossil fuel o Wind ­ Gravity o Tides­ o Falling water ­ Chemical Reactions ­ Nuclear Fission ­ Geothermal – happens in the center of the Earth Oil and Natural Gas ­ Hydrocarbon compounds ­ Remains of marine algae and plankton 90 ­ oil shale o black organic shale 160 ­ oil and natural gas 250 ­ natural gas Oil window is from 90 – 160 degrees Celsius Oil and Natural Gas Trap ­ Source rock­ organic rich shale ­ Reservoir rock: high porosity and permeability o Sponge o Porosity­ bunch of holes o Permeability­ holes next to each other ­ Seal Rock Where is oil found ­ Anticline ­ Fault ­ Salt dome ­ Stratigraphic Finding Oil and Natural Gas ­ Generate seismic waves ­ Look for folds Extracting Oil and Natural Gas ­ Drilling o Puncture the seal rock ­ Pumping o Brings oil to the surface Refining Oil ­ Crude oil is distilled ­ Process depends on grade o Sulfur content o Specific gravity Products made from a barrel of crude oil ­ Diesel 12 ­ Jet fuel 4 ­ Other product 7 ­ Gasoline 19 ­ Petroleum gas 2 Other types of Formations/ extractions ­ Tar Sands o Viscous oil in sand o Cannot pump  Mined then heated  Heated then pumped o Very expensive ­ Oil Shale o Has not reached oil window o Mined then heated o Very expensive ­ Fracking o Hydraulic fracturing  Extracting natural gas o Increases well production o Drawbacks  Groundwater contamination  Land use issues Running out of oil ­ Other sources exist o Liquefied coal o Oil shale o Tar sands o Methane hydrate ­ Not economically viable at current prices and technology When will we run out of oil ­ Geologist o Soon ­ Economists o Will stop using it first Coal ­ Plant material buried o Low oxygen o Water squeezed out o 50 % C= Peat o 70 % C= coal Coal Production ­ Coal not made all the time ­ Plenty of coal for now Coal Extraction ­ Strip mining o Coal < 100 m ­ Underground mining o Coal > 100m o Very dangerous Drawbacks of Fossil Fuels ­ Air pollution o Particles and gases o Acid rain ­ Carbon dioxide o Greenhouse gas ­ Byproducts o Mine runoff ­ Spills o Groundwater o Ocean ­ Fatalities in mines o A lot Alternate Energy Sources ­ 90% of world energy needs from non renewable fossil fuels ­ Possible alternate energy sources o We cover 5 Nuclear Power ­ Energy release when nucleus is split (fission) ­ Drawback o Controlling nuclear reactions  Lot of work and planning  Potential meltdown o Nuclear waste  Damaging to living organisms  Long time decay (decades­ centuries) Wind ­ Must have steady breeze ­ Clean ­ Drawbacks o Noisy o Ugly o Hazard to wildlife Solar ­ Sunlight converted to electricity ­ Clean ­ Drawbacks o Not efficient o Not cost effective Hydroelectric ­ Two kinds o River  No pollutants  Drawbacks  Dams o Tidal  No pollutants  Drawback  Construction Geothermal ­ Use Earths eternal heat where it comes near surface ­ Use in two ways o Water o Steam to turn turbines ­ Drawbacks o Conditions limited ­

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Chapter 1.4, Problem 28 is Solved
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Textbook: Fundamentals of Probability, with Stochastic Processes
Edition: 3
Author: Saeed Ghahramani
ISBN: 9780131453401

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Let A1, A2, A3, ... be a sequence of events of a sample