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Advanced Topics in Probability and Stochastic Processes

A solved assignment covering advanced concepts in probability and stochastic processes.

Ethan Wilson
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Advanced Topics in Probability and Stochastic Processes1. Linear Transformations of Normal Random Variables are also Normal()()()()()()()()()()2222222Let~,and,11The p.d.f of,exp,,0.2211The c.d.f of,exp22LetThe c.d.f of,11exp22XxXYXNa bXfxxxX FxPXxtdtYaXbY FyP YyP aXbyybPXat −=−−−  ==−−=+==+−==−−()2222211exp22Therefore,has also normal distribution with parameters,.ybatdtyabdyaaYab a−−−=−−++

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