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# lecture%204_complete - APPENDIX B Fundamentals of...

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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 ?¡ ? = ? + ??, ℎ¢ ?~(? + ?, ? 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_complete - APPENDIX B Fundamentals of...

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