lecture%204_s

lecture%204_s - APPENDIX B Fundamentals of probability...

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Unformatted text preview: APPENDIX B Fundamentals of probability (cont.) Some common continuous random variables 1. THE NORMAL DISTRIBUTION The Normal distribution describes the probability distribution for a random variable X that has the following properties: X can take any value on the real line (, ) The pdf of X has the familiar bell shaped curve If ? = ? ? = 2 , then the pdf for X can be written as: ? = 1 exp 2 2 , < < ~(, 2 ) 1. THE NORMAL DISTRIBUTION 2. THE STANDARD NORMAL DISTRIBUTION The Normal distribution has some very nice properties. One of them is that a linear function of a normal random variable is also normal. Hence, if ?~ , 2 ? ? = ? + ??, ?~(? + ?, ? 2 2 ) So ? = ~(0,1) i.e. Z has a standard normal distribution. The pdf of a standard normal random variable Z is given by: = 1 exp 2 , < < 2. WHY IS THE STANDARD NORMAL DISTRIBUTION SO USEFUL?...
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lecture%204_s - APPENDIX B Fundamentals of probability...

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